OPINION AND ORDER
Plaintiff Frankart Distributors, Inc. (“Frankart”) sues defendant Federal Insurance Company (“Federal”) to recover attorneys’ fees incurred by Frankart when Federal allegedly wrongfully refused to defend Frankart in a lawsuit. The action is before the Court on cross-motions for summary judgment.
The parties have stipulated to the material facts, which are as follows. Federal issued to Frankart a Commercial Umbrella Liability Policy, number 7923-34-04 (“the Policy”), which was effective at all relevant times herein. The Policy provided excess insurance over any other “underlying” policy held by Frankart, and covered:
all sums ... for which the insured shall become obligated to pay by reason of liability
(a) imposed upon the insured by law or
(b) assumed under contract or agreement by the insured,
arising out of personal injury, property damage or advertising liability caused by an occurrence.
See Stipulated Facts, Exhibit A at if 1 (emphasis in original).
The policy defines an occurrence as:
an accident, including continuous or repeated exposure to conditions, which results in personal injury, property damage or advertising liability neither expected nor intended from the standpoint of the insured.
Id. at 5 (emphasis in original).
An “endorsement” dated January 30, 1975 provided that the policy excluded coverage of any “[l]oss, damage or expense caused intentionally by or at the direction of the insured.” Id. (emphasis in original).
The policy also provided that:
With respect to any occurrence not covered by the underlying policies ... but covered by the terms and conditions of this policy the Company shall, in addition to the amount of ultimate net loss payable;
(1) defend any suit against the insured seeking damages on account of personal injury, property damage or advertising liability, even if any of the allegations of the suit are groundless, false or fraudulent; ...
Id. at 114(b) (emphasis in original).
In April 1978 a suit was commenced against Frankart and others in the Eastern District of New York. The complaint alleged, inter alia, that Frankart “knowingly aided and abetted and conspired with [others] in the breach of fiduciary obligations to plaintiffs, in the conversion of ... funds and other assets, and in defrauding plaintiffs, ...” See Stipulated Facts, Exhibit C at U 20. Frankart’s other insurer, Eagle Star Insurance Co., with whom Frank-art had an “underlying policy” within the meaning of the Federal policy, declined to defend the action because the allegations against Frankart did not fall within the coverage of the Eagle Star policy. Upon notification that Eagle Star disclaimed coverage, Frankart forwarded a copy of the summons and complaint to Federal.
On May 11, 1978 Federal wrote to Fran-kart to confirm receipt of the summons and complaint, and noted that the allegations of the complaint all apparently fell within the above-mentioned exclusion regarding losses intentionally caused. Therefore, Federal stated that Frankart would be personally liable for any judgment against it. Federal went on to advise that the legal papers had been referred to a law firm “to defend you in this .action.” Finally, the letter provided that:
Not withstanding the specific portions of the policy referred to in this letter, all rights are reserved both to Frankart Dis*591tributors, Inc. and the Federal Insurance Company as though the policy were set forth in full herein.
See Stipulated Facts, Exhihit E.
On June 7, 1978, Federal wrote to Fran-kart again, stating that this letter supplemented that of May 11, 1978. Federal cited to the coverage provisions of the Policy, and stated that further investigation had revealed that the loss claimed in the Eastern District complaint was not encompassed by the Policy. Therefore, Federal advised Frankart that it would instruct its attorneys to return the legal papers to Frankart for Frankart to handle personally and at its own expense. See Stipulated Facts, Exhibit F. On June 8, 1978 Federal returned the summons and complaint to Frankart with a cover letter which once again contained a reservation of rights. See Stipulated Facts, Exhibit G. The Eastern District lawsuit was thereafter defended by Frankart’s personal counsel, and was eventually settled.
Frankart sues Federal only for the attorneys’ fees incurred in defending the Eastern District action, and not for any amount paid by Frankart in settlement of that lawsuit. The complaint herein claims three grounds for recovery. First, Frankart sues for breach of Federal’s contractual duty to defend pursuant to the Policy. Second, Frankart argues that even if Federal was not bound by the Policy to defend the Eastern District lawsuit, Federal had “waived such policy provision ... based upon its action in this matter.” See Complaint at II Seventeenth. Third, Frankart alleges that Federal should be estopped from claiming it had no duty to defend.
1. Contract claim
It is well settled that an insurer has a duty to defend any claim against its insured which, if proved to be true, would give rise to liability under the insurance contract. See, e.g., Sturges Manufacturing Co. v. Utica Mutual Insurance Co., 37 N.Y.2d 69, 72, 332 N.E.2d 319, 321, 371 N.Y.S.2d 444, 447 (1975); Goldberg v. Lumber Mutual Casualty Insurance Co., 297 N.Y. 148, 154, 77 N.E.2d 131, 133 (1948); Parkset Plumbing and Heating Corp. v. Reliance Insurance Co., 87 A.D.2d 646, 647, 448 N.Y.S.2d 739, 740 (2d Dept.1982) (mem.); Touchette Corp. v. Merchants Mutual Insurance Co., 76 A.D.2d 7, 9-10, 429 N.Y.S.2d 952, 954 (4th Dept.1980). The fact that the allegations are false or unfounded does not relieve the insurer of its obligation to defend. See, e.g., Lionel Freedman, Inc. v. Glens Falls Insurance Co., 27 N.Y.2d 364, 368, 267 N.E.2d 93, 94, 318 N.Y.S.2d 303, 305 (1971). However, assuming the allegations of the complaint to be true, if there is no factual or legal basis upon which the insurer could be liable the insurer need not undertake the defense. See, e.g., Syoor-Lasher Co. v. Aetna Casualty and Surety Co., 39 N.Y.2d 875, 876, 352 N.E.2d 139, 140, 386 N.Y.S.2d 221, 222 (1976) (mem.); Lionel Freedman, supra, 27 N.Y.2d at 368, 267 N.E.2d at 94, 318 N.Y.S.2d at 305; Prudential Lines, Inc. v. Firemen’s Insurance Co., 91 A.D.2d 1, 5, 457 N.Y.S.2d 272, 275 (1st Dept.1982); Touchette, supra, 76 A.D.2d at 10, 429 N.Y.S.2d at 954.
The duty to defend is contractual in nature, is incident to the primary obligation of liability for covered occurrences, and is dependent upon and supplemental to that primary obligation. See, e.g., Lionel Freedman, supra, 27 N.Y.2d at 367, 267 N.E.2d at 94, 318 N.Y.S.2d at 304; 7C J. Appleman, Insurance Law and Practice § 4681, at 8-9, § 4682, at 26, § 4684, at 72-73, 86, § 4684.01, at 91-92, § 4686, at 165 (Berdal ed. 1979). Therefore, there is no duty to defend where the alleged basis for liability is not within the coverage of the policy, including where the alleged conduct falls within an express policy exclusion. See, e.g., International Payer Co. v. Continental Casualty Co., 35 N.Y.2d 322, 325, 320 N.E.2d 619, 621, 361 N.Y.S.2d 873, 875 (1974); Parkset, supra, 87 A.D.2d at 647, 448 N.Y.S.2d at 740.1 The issue of *592coverage is a matter of law for the Court. See, e.g., National Union Fire Insurance Co. v. Medical Liability Mutual Insurance Co., 85 A.D.2d 851, 852, 446 N.Y.S.2d 480, 482 (3d Dept. 1981) (mem.); Touchette, supra, 76 A.D.2d at 9, 429 N.Y.S.2d at 954.
The Policy at issue herein covers losses caused by accident neither expected nor intended by Frankart and resulting in personal injury, property damage or advertising liability, and expressly excludes coverage of losses intentionally caused by or at the direction of Frankart. This clearly excludes from coverage any loss allegedly caused by Frankart’s knowing or fraudulent conduct. Therefore, even assuming the allegations of the Eastern District complaint were true, Federal had no potential liability under the Policy, and therefore no incident duty to defend.
2. Waiver
Plaintiff argues that, even if the Policy did not cover the claims alleged in the Eastern District fraud action, Federal “did not choose to invoke its right not to defend.” See Plaintiffs Memorandum of Law in Support of Plaintiff’s Motion For Summary Judgment at 4. Instead, by sending the May 11, 1978 letter, Frankart contends that Federal “informed FRAN-KART that it would take up the defense ____[and that] [t]his act constituted a waiver of FEDERAL’s right not to defend FRANKART.” See id. Frankart contends that “by reason of the waiver with knowledge, the duty to defend arose” and that “FEDERAL ‘breached’ that duty by its June 7th letter notifying FRANKART that it would not defend____” See id. at 7.
It is clear that while defenses to coverage based upon the insured’s failure to comply with the terms of the policy may be waived by the insurer by failure to timely raise them, see, e.g., Schiff, supra, 51 N.Y.2d at 698, 417 N.E.2d at 87, 435 N.Y.S.2d at 975; Draper v. Oswego County Fire Relief Association, 190 N.Y. 12, 16-17, 82 N.E. 755, 756 (1907); Kiernan v. Duchess County Mutual Insurance Co., 150 N.Y. 190, 195, 44 N.E. 698, 699 (1896), the doctrine of waiver cannot be used to create coverage where none previously existed under any insurance contract. See, e.g., Schiff, supra, 51 N.Y.2d at 698, 417 N.E.2d at 87, 435 N.Y.S.2d at 975; Draper, supra, 190 N.Y. at 17, 82 N.E. at 756; National Union, supra, 85 A.D.2d at 852, 446 N.Y.S.2d at 482; Van Wyck Associates v. St. Paul Fire & Marine Insurance Co., 115 Misc.2d 447, 451-52, 454 N.Y.S.2d 266, 270 (Sup.Ct.1982). “[W]here the issue is the existence or nonexistence of coverage ... the doctrine of waiver is simply inapplicable.” Schiff, supra, 51 N.Y.2d at 698, 417 N.E.2d at 87, 435 N.Y.S.2d at 975. Since the duty to defend is incident to coverage, that duty also cannot be created by waiver.
Frankart argues that a duty to defend was created here where none had previously existed, because defendant did not refuse to defend Frankart in its first letter of May 11, 1978. This is clearly contrary to the well-established law of waiver cited above, especially since, in addition to noting the intentional conduct exclusion in its May 11, 1978 letter disclaiming liability under the Policy, Federal also specifically reserved all its rights under the Policy. Therefore, Federal cannot be held to have waived any other Policy provision. See, e.g., Schiff, supra, 51 N.Y.2d at 700, 417 N.E.2d at 88, 435 N.Y.S.2d at 976.
Counsel to Frankart admitted at oral argument that it knows of no decision in New York where a court awarded attorneys’ fees to an insured on a theory of waiver under facts such as those in this case. Moreover, even if a doctrine of waiver applied herein, the Court finds that Federal’s May 11, 1978 letter was insufficient to con*593stitute a voluntary and intentional relinquishment by Federal of any known right not to defend, see, e.g., Schiff, supra, 51 N.Y.2d at 698, 417 N.E.2d at 87, 435 N.Y. S.2d at 975; Draper, supra, 190 N.Y. at 16, 82 N.E. at 756, especially in light of Federal’s reservation of rights. Frankart points to no other fact or action by Federal to support its waiver argument.
3. Estoppel
In its complaint Frankart alleges that by initially undertaking the defense of the fraud action, Federal was “estopped to raise the terms and conditions of the policy” and therefore could not later withdraw from defending Frankart.
It is well settled that where an insurer assumes the defense of its insured it may be estopped from later refusing to continue to defend, despite noncoverage, where such refusal would prejudice the rights of the insured. See, e.g., Schiff, supra, 51 N.Y.2d at 699, 417 N.E.2d at 87, 435 N.Y.S.2d at 975; O’Dowd v. American Surety Co., 3 N.Y.2d 347, 355, 144 N.E.2d 359, 363, 165 N.Y.S.2d 458, 463 (1957); Gerka v. The Fidelity & Casualty Co., 251 N.Y. 51, 57, 167 N.E. 169, 170 (1929); Touchette, supra, 76 A.D.2d at 12, 429 N.Y.S.2d at 955.
Federal notified Frankart of its refusal to defend less than a month after it received the complaint. Plaintiff has not even attempted to support its estoppel argument by any particularized showing of prejudice resulting from Federal’s conduct. Indeed, plaintiff’s counsel conceded at oral argument that given the facts of this case, Frankart could not demonstrate any prejudice by Federal’s refusal to defend, and agreed with the Court that plaintiff therefore cannot prevail on a theory of estoppel.
It follows that defendant is entitled to summary judgment on each claim alleged in the complaint.
It is SO ORDERED.