Plaintiff-appellant Aviall is a former wholly-owned subsidiary of defendant-appellee Ryder. Following a spin-off of Aviall to Ryder’s shareholders, Aviall disputed Ryder’s allocation of certain pension-related assets and liabilities in the spin-off. Pursuant to the contract governing the spin-off, Aviall sought arbitration of the dispute before KPMG Peat Marwick (“KPMG”), Ryder’s outside auditor. Subsequently, however, Av-iall brought this suit in the Southern District of New York (Michael B. Mukasey, J.) to disqualify KPMG as arbitrator, claiming that KPMG was partial to Ryder on account of its business relationship with Ryder, and that KPMG had assisted Ryder in preparing for the arbitration. Judge Mukasey granted summary judgment to Ryder, Aviall, Inc. v. Ryder System, Inc., 913 F.Supp. 826 (S.D.N.Y.1996), and Aviall appeals. We affirm.
Ryder operates a variety of transportation businesses, which for many years included businesses that provided aviation services. In June of 1993, Ryder decided to divest itself of its aviation-related businesses. In December 1993, after consolidating those businesses in Aviall, Ryder spun off Aviall to Ryder’s shareholders. The terms of the spin-off were set forth in a Distribution and Indemnity Agreement and three other documents (collectively, the “Spin-Off Documents”) executed by the two companies. Although Aviall was not able to negotiate the terms of the Distribution Agreement, which was signed on Aviall’s behalf by a Ryder *894officer, the Ryder officer was also an officer and director of Aviall. Aviall’s directors unanimously consented to the Distribution Agreement.
Under the Distribution Agreement, Aviall was intended to have a net worth of $314 million at the time of the spin-off. Section 3.03 of the Distribution Agreement therefore provided for preparation of a Distribution Statement, which would set forth the amount of dividends and debt repayments from Av-iall to Ryder necessary to reduce Aviall’s net worth to the intended amount. Section 3.03(c) provides that
[i]f there are any items related to the Distribution Statement which are in dispute, then such items shall be submitted to KPMG Peat Marwick ... for resolution.
At the time, KPMG was outside auditor to both companies. Shortly after the spin-off, however, Aviall replaced KPMG with a different outside auditor.
Section 3.03(c) differs from provisions in the Spin-Off Documents for resolution of other disputes. Under section 3.11(n) of the Distribution Agreement, for example, any dispute over the amount owed by Aviall to Ryder from the proceeds of the sale of certain Aviall businesses is to be submitted to KPMG only
if, at the time of such dispute, [KPMG] are the independent auditors for both Ryder and Aviall.... If, at the time of such dispute, [KPMG] are not the independent auditors for both Ryder and Aviall, then the parties shall select another nationally recognized certified public accounting firm, which does not serve as independent auditors for either Ryder or Aviall, to resolve any such dispute.
Similarly, under section 5.04 of another SpinOff Document, the Tax Sharing Agreement, any disputes relating to that agreement “shall be resolved by a ‘Big Six’ public accounting firm or a law firm satisfactory to Ryder and Aviall.”
Ryder had originally intended to transfer to Aviall all pension assets, obligations, and expenses associated with Aviall employees. Because the pension plan was underfunded, however, the Pension Benefit Guaranty Corporation refused to permit such a transfer. Ultimately, under the Distribution Agreement Ryder retained all pension assets and obligations of Aviall employees up to the date of the spin-off, while Aviall would be responsible for all post-divestiture pension benefits. Ryder therefore recorded the Aviall pension liabilities it assumed as a prepaid expense asset on Aviall’s balance sheet. This increased by $17.6 million the amount Aviall transferred to Ryder to reduce Aviall’s net worth to its intended amount.
Before settling on this accounting treatment, Ryder discussed the issue with Richard Hamlin, its engagement partner in KPMG’s Miami office, and Hector Mojena, Hamlin’s then-senior manager and now partner. Hamlin and Mojena in turn asked KPMG’s Department of Professional Practice in New York to approve the treatment, and John Deming of that department prepared a Record Of Inquiry which did so. Hamlin and Mojena eventually certified Ryder’s 1993 financial statements, while Bruce Piller of KPMG’s Dallas office did the same for Av-iall’s statements. In December 1993 the spin-off was executed, and shortly thereafter Aviall replaced KPMG as its independent auditor.
In November 1994, Aviall informed KPMG that it disputed the allocation of the pension benefits and, pursuant to section 3.03(c), requested that KPMG arbitrate the dispute. Andrew Capelli, a partner in KPMG’s Department of Professional Practice, was selected to arbitrate the dispute, apparently by Hamlin, KPMG’s Ryder engagement partner. Capelli drafted and signed an engagement letter which represented that
certain partners and employees of [KPMG] have or had an existing or prior relationship with Ryder and Aviall but will in no way be involved in this engagement in any manner.
The letter also represented that “there will be no exparte [sic] communications with respect to any aspect of this engagement.” The parties never signed the letter, however, because in early December Aviall requested that KPMG withdraw as arbitrator.
About this time, Hamlin — now a member of KPMG’s board of directors — contacted Ca-*895pelli seeking names of pension accounting experts that Ryder might consult. Capelli, who may have been unsure of the purpose for which Hamlin sought the names, provided the names of two people who sat with him on the American Institute of Certified Public Accountants Employee Benefit Plans Committee. Hamlin, Mojena, and Deming also provided some unspecified assistance to Ryder in preparing for the arbitration. In late 1994, Piller, the KPMG partner who certified Aviall’s 1993 year-end financials incident to the spinoff, also provided confidential papers from Aviall’s file to Hamlin and Mojena, both of whom he knew to be assisting Ryder in connection with the arbitration. KPMG’s assistance in connection with the arbitration ceased around the beginning of 1995, shortly after Aviall requested that KPMG withdraw. Except for the conversation with Hamlin regarding experts, Capelli had no contact with Hamlin or anyone else concerning the merits of the dispute.
In February 1995, after KPMG refused to withdraw as arbitrator, Aviall filed a complaint seeking a declaration that KPMG could not arbitrate the underlying dispute. Ryder then moved to dismiss the complaint under Fed.R.Civ.P. 12(b)(6), or, in the alternative, to stay the litigation pending the outcome of arbitration. Following discovery and before disposition of the 12(b)(6) motion, Aviall moved for summary judgment and Ryder cross-moved for summary judgment. On February 7, 1996, the district court granted summary judgment for Ryder. Judge Muka-sey held that Aviall’s action was premature because the Federal Arbitration Act (the “FAA”), 9 U.S.C. § 1 et seq., permits pre-award removal of an arbitrator only “when the court concludes that one party has deceived the other, that unforeseen intervening events have frustrated the intent of the parties, or that the unmistakable partiality of the arbitrator will render the arbitration a mere prelude to subsequent litigation.” 913 F.Supp. at 836. He also ruled that even were the “evident partiality” standard for vacatur of an award under § 10(a)(2) of the FAA to apply, Aviall had not demonstrated that KPMG was evidently partial. 913 F.Supp. at 835-36.
On appeal, Aviall argues that KPMG’s relationship with Ryder as its regular outside auditor, as well as KPMG’s conduct in connection with this dispute since it arose, demonstrate partiality which disqualifies KPMG from arbitrating the dispute. We agree with the district court that neither KPMG’s relationship with Ryder, nor its conduct in connection therewith, is a valid ground for removing KPMG before an award has been rendered.
This dispute is governed by the FAA, under which
' [a] written provision in any ... contract evidencing a transaction involving commerce to settle by arbitration a controversy thereafter arising out of such contract or transaction ... shall be valid, irrevocable, and enforceable, save upon such grounds as exist at law or in equity for the revocation of any contract.
9 U.S.C. § 2. Although the FAA provides that a court can vacate an award “[wjhere there was evident partiality or corruption in the arbitrators,” id. § 10(a)(2), it does not provide for pre-award removal of an arbitrator. Thus, an agreement to arbitrate before a particular arbitrator may not be disturbed, unless the agreement is subject to attack under general contract principles “as exist at law or in equity.” Id. § 2. Indeed, we have stated in dicta that “it is well established that a district court cannot entertain an attack upon the qualifications or partiality of arbitrators until after the conclusion of the arbitration and the rendition of an award.” Michaels v. Mariforum Shipping, S.A., 624 F.2d 411, 414 n. 4 (2d Cir.1980); see also Florasynth, Inc. v. Pickholz, 750 F.2d 171, 174 (2d Cir.1984) (“The Arbitration Act does not provide for judicial scrutiny of an arbitrator’s qualifications to serve, other than in a proceeding to confirm or vacate an award, which necessarily occurs after the arbitrator has rendered his service.”) District courts within this circuit have so held on at least two occasions. See Alter v. Englander, 901 F.Supp. 151, 153 (S.D.N.Y.1995); Marc Rich & Co. v. Transmarine Seaways Corp., 443 F.Supp. 386, 387 (S.D.N.Y.1978).
Although Aviall points to cases in which an arbitrator was removed prior to arbitration *896on account of a relationship with one party to the dispute, see Erving v. Virginia Squires Basketball Club, 349 F.Supp. 716 (E.D.N.Y.), aff'd, 468 F.2d 1064 (2d Cir.1972); Masthead Mac Drilling Corp. v. Fleck, 549 F.Supp. 854 (S.D.N.Y.1982); Cristina Blouse Corp. v. International Ladies Garment Workers’ Union, Local 162, 492 F.Supp. 508 (S.D.N.Y.1980), those cases simply manifest the FAA’s directive that an agreement to arbitrate shall not be enforced when it would be invalid under general contract principles. In Erv-ing, for example, the basketball star Julius Erving had entered into a contract which provided for arbitration by the Commissioner of the American Basketball Association. When the dispute arose, a new Commissioner — who was a partner of the law firm representing the defendant — had been appointed, resulting in frustration of the parties’ contractual intent to submit their dispute to a neutral expert. Accordingly, the district court reformed the contract by substituting a neutral arbitrator in the Commissioner’s stead. 349 F.Supp. at 719. See Marc Rich, 443 F.Supp. at 388 (distinguishing Erving as a case of reformation).
Similarly, in Masthead Mac, the contractually-designated arbitrators were business associates of the defendant. The plaintiff, however, claimed not that the FAA allows automatic removal of such an arbitrator, as Aviall claims here, but that defendant fraudulently induced the plaintiff to enter into the contract by concealing the arbitrators’ relationship with the defendant. Therefore, the district court — ultimately with the consent of both parties — designated a neutral arbitrator. 549 F.Supp. at 856; see also Cristina Blouse, 492 F.Supp. at 510-11 (reforming contract to remove arbitrator who, undisclosed to plaintiff, was former lawyer for defendant).
The only case cited by Aviall in which the court removed an arbitrator whose relationship to one party was disclosed and foreseen is Third Nat’l Bank v. WEDGE Group Inc., 749 F.Supp. 851 (M.D.Tenn.1990). In WEDGE, the arbitration provision at issue provided that the dispute would be submitted for resolution “to the certified public accounting firm retained by WEDGE at the time of such referral.” Id. at 853 n. 1. The plaintiff objected to arbitration, asserting, inter alia, that Ernst & Young, the accountant so designated, would be unable to render an unbiased award on account of its fiduciary duty to WEDGE. The court allowed arbitration to proceed, subject to appointment of a neutral arbitrator. Id. at 855. Like the district court, we do not find WEDGE persuasive. In support of its determination that Ernst & Young could be removed as arbitrator, the WEDGE court cited as authority only our decision in Erving, and Masthead Mac. As our discussion above indicates, however, we do not read those decisions as supporting the result in WEDGE. Rather, the touchstone in each of those cases was that the arbitrator’s relationship to one party was undisclosed, or unanticipated and unintended, thereby invalidating the contract.
Here, in contrast, Aviall was fully aware of KPMG’s relationship with Ryder when the Distribution Agreement was executed. The Distribution Agreement also clearly contemplated that KPMG would arbitrate the dispute even were it no longer to be outside auditor to both companies; unlike § 3.11(n), or § 5.04 of the Tax Sharing Agreement, § 3.03(c) designates KPMG regardless of whether it is outside auditor to both, or either, of the companies. Admittedly, as a wholly-owned subsidiary, Aviall played no role in the drafting of the Distribution Agreement and had no power to bargain over its terms. But that in no way points to any infirmity in the contracting process, for Ryder was obligated to draft those terms in the manner most advantageous to its shareholders, who would also be the shareholders of Aviall immediately following the spin-off. See Anadarko Petroleum Corp. v. Panhandle Eastern Corp., 545 A.2d 1171 (Del.1988) (in spin-off transaction, officers of subsidiary owe fiduciary duty only to parent corporation, and neither parent nor subsidiary’s officers owe duty to prospective stockholders of subsidiary). Thus, Aviall can hardly object to the Distribution Agreement being enforced according to its terms. See Merit Ins. Co. v. Leatherby Ins. Co., 714 F.2d 673, 679 (7th Cir.1983) (“The parties to an arbitration choose their method of dispute resolution, and can ask no more impartiality than in*897heres in the method they have chosen”) (internal quotation marks omitted), modified on other grounds, 728 F.2d 943 (7th Cir.1984); cf. Westinghouse Elec. Corp. v. New York City Transit Auth., 82 N.Y.2d 47, 603 N.Y.S.2d 404, 623 N.E.2d 531 (1993) (arbitration agreement designating employee of a party to the dispute as arbitrator is not against New York public policy).
The FAA’s lack of provision for pre-award removal of an arbitrator likewise prevents us from removing KPMG on account of whatever assistance it may have lent to Ryder so far in connection with the arbitration. Aviall points us to no authority to the contrary. Thus, Aviall’s evidence of any such conduct by KPMG is not material, and cannot defeat Ryder’s summary judgment motion. See Anderson v. Liberty Lobby, Inc., 477 U.S. 242, 248,106 S.Ct. 2505, 2510, 91 L.Ed.2d 202 (1986) (“As to materiality ... [o]nly disputes over facts that might affect the outcome of the suit under the governing law will properly preclude the entry of summary judgment.”) Aviall, of course, remains free to challenge on the ground of evident partiality any award ultimately rendered by KPMG. See 9 U.S.C. § 10(a)(2).
In this regard, Aviall expresses fear that because the district court ruled as a matter of law that KPMG’s conduct did not constitute evident partiality, Ryder might attempt to use that ruling to preclude Aviall from bringing a post-award challenge. We think this concern is unfounded, because Judge Mukasey’s findings would not be binding in any future proceeding, whether under the doctrine of issue preclusion or as law of the case.
Under New York law, which the parties designated in the Distribution Agreement’s choice-of-law provision, issue preclusion applies only if the issue was “clearly raised in a prior proceeding and decided against [the party to be precluded] where the party to be precluded had a full and fair opportunity to contest the prior determination.” Weiss v. Manfredi, 83 N.Y.2d 974, 976, 616 N.Y.S.2d 325, 639 N.E.2d 1122 (1994). Any attempt to grant preclusive effect to the district court’s evident partiality ruling would fail both prongs of this test.
First, in order for the issue to have been clearly raised and decided, it “must have been material to the first action or proceeding and essential to the decision rendered therein.” Ryan v. New York Tel. Co., 62 N.Y.2d 494, 500, 478 N.Y.S.2d 823, 467 N.E.2d 487 (1984). Here, Judge Mukasey had already correctly determined that the FAA gave him no authority to remove KPMG for its conduct. As such, his further ruling that Aviall had not shown evident partiality on KPMG’s part “if [that standard] did apply at this stage of the proceedings,” 913 F.Supp. at 835, was in no way essential to his decision. See Fletcher v. Atex, Inc., 68 F.3d 1451, 1457 (2d Cir.1995) (refusing to give preclusive effect, under New York law, to finding which was not essential to the prior judgment).
Additionally, as we have recently noted, a party cannot be considered to have had a full and fair opportunity to litigate an issue, and issue preclusion cannot apply, “if there is an inability to obtain [appellate] review or there has been no review, even though an appeal was taken.” Johnson v. Watkins, 101 F.3d 792, 795 (2d Cir.1996). As we have no occasion to review Judge Mukasey’s findings, they cannot have any preclusive effect in any subsequent action. See also Gelb v. Royal Globe Ins. Co., 798 F.2d 38, 45 (2d Cir.1986) (“if an appeal is taken and the appellate court affirms on one ground and disregards the other, there is no collateral estoppel as to the unreviewed ground”).
Judge Mukasey’s findings likewise would not be binding as law of the ease. Under the doctrine of law of the case, “ ‘a legal decision made at one stage of litigation, unchallenged in a subsequent appeal when the opportunity to do so existed, becomes the law of the ease for future stages of the same litigation, and the parties are deemed to have waived the right to challenge that decision at a later time.’ ” North River Ins. Co. v. Philadelphia Reinsurance Corp., 63 F.3d 160, 164 (2d Cir.1995) (quoting Williamsburg Wax Museum, Inc. v. Historic Figures, Inc., 810 F.2d 243, 250 (D.C.Cir.1987)), cert. denied, — U.S. -, 116 S.Ct. 1289, 134 L.Ed.2d 233 (1996). Aviall, however, did not *898let the district court’s findings go unchallenged; rather, it vehemently challenged them at the very first opportunity for appeal. It therefore cannot in any way be deemed to have waived the right to challenge them later. Ordinarily, of course, a timely challenge on appeal leads to a resolution which would foreclose the need for any future challenge. But, as with issue preclusion, when there has been no review even though an appeal has been taken, it is equivalent to the party not having had an opportunity to appeal, and prevents the challenged decision from becoming the law of the case. As we have not passed upon the challenged findings, they cannot become the law of the case and Aviall will not be bound by them in any future stage of the proceedings. We therefore affirm the judgment of the district court.