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                                                                     Exhibit 4.4


                                Amendment to the
                        Endurance Specialty Holdings Ltd.
                          Warrant for Ordinary Shares,
                               dated July 22, 2002

            WHEREAS, as a result of certain amendments to the Bye-Laws of
Endurance Specialty Holdings Ltd. ("Company"), it is necessary to amend certain
provisions of the Endurance Specialty Holdings Ltd. Warrant for Ordinary Shares
("Warrant"); and

            WHEREAS, the terms and provisions of the Warrant for Ordinary Shares
may be modified, waived or otherwise amended by a written agreement between the
Company and a Warrant Holder that is consented to in writing by all other
Warrant Holders.

            NOW, THEREFORE, it is hereby agreed as follows:

            1. Capitalized Terms. Capitalized terms used and not otherwise
defined herein shall have the meaning set forth in the Warrant.

            2. Conditions to Issuance of Ordinary Shares and Issuance of Class A
Shares. Section 4.1 of the Warrant is hereby amended and restated as follows:

            "Conditions to Issuance of Ordinary Shares and Issuance of Class A
Shares. The Warrant Holder acknowledges and agrees that this Warrant may be
exercised for Ordinary Shares only if (i) such exercise would not cause any
Person to become a 9.5% Shareholder (without giving effect to the provisions of
the Endurance Bye-Laws that might limit the voting power in Endurance or ESIL
attributable to Shares held by the Warrant Holder) or (ii) all Shareholders who
are affected consent thereto. The Warrant Holder shall receive Class A Shares
upon exercise hereof at any time when this Warrant may not be exercised for
Ordinary Shares by virtue of the limitations contained in the immediately
preceding sentence."

            3. Controlled ESIL Shares. The definition of "Controlled ESIL
Shares" in Section 8.1 of the Warrant is hereby amended and restated as follows:

            " 'Controlled ESIL Shares' in reference to any Person shall mean all
ESIL Shares that such Person is deemed to own directly, indirectly (within the
meaning of Section 958(a) of the Code) or, in the case of any U.S. Person,
constructively (within the meaning of Section 958(b) of the Code)."

            4. Controlled Shares. The definition of "Controlled Shares" in
Section 8.1 of the Warrant is hereby amended and restated as follows:

            " 'Controlled Shares' in reference to any Person shall mean all
Ordinary Shares that such Person is deemed to own directly, indirectly (within
the meaning of
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Section 958(a) of the Code) or, in the case of any U.S. Person, constructively
(within the meaning of Section 958(b) of the Code)."

            5. Excess Shareholder. The definition of "Excess Shareholder" in
Section 8.1 of the Warrant is hereby deleted in its entirety.

            6. Maximum Percentage. The definition of "Maximum Percentage" in
Section 8.1 of the Warrant is hereby deleted in its entirety.

            7. 9.5% Shareholder. Section 8.1 of the Warrant is hereby amended by
adding the following definition thereto:

            " '9.5% Shareholder' shall mean a Person that owns (i) Ordinary
Shares (within the meaning of Section 958(a) of the Code) and owns or is deemed
to own Controlled Shares which confer votes in excess of 9.5% (or such other
percentage as determined under section 69(3) of the Endurance Bye-Laws) of the
votes conferred by all of the issued and outstanding Ordinary Shares or (ii)
ESIL Shares (within the meaning of Section 958(a) of the Code) and owns or is
deemed to own Controlled ESIL Shares which confer votes in excess of 9.5% (or
such other percentage as determined under section 69(3) of the Endurance
Bye-Laws) of the votes conferred by all of the issued and outstanding ESIL
Shares directly or indirectly within the meaning of Section 958(a) of the Code."

            8. Consent. The undersigned Warrant Holder hereby consents to
Amendments, on the terms and conditions set forth herein, to each Warrant for
Ordinary Shares, dated July 22, 2002, issued by the Company.

            9. Execution of Amendment. (a) This Amendment may be executed in
counterparts of like form, each of which, when executed, shall be deemed to be
an original and all of which taken together shall constitute one and the same
instrument.

            (b) This Amendment shall be effective immediately following the
closing of an initial public offering of the Company's Shares.

            (c) Except as hereby amended, the terms and provisions of the
Agreement shall remain in full force and effect.


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         IN WITNESS WHEREOF, the undersigned have hereunto set their hand as
of the ___ day of ____, 2003.



                                        ENDURANCE SPECIALTY
                                        HOLDINGS LTD.

                                        By:
                                           -------------------------------
                                           Name:
                                           Title:



                                        [SHAREHOLDER]

                                        By:
                                           -------------------------------
                                           Name:
                                           Title: