FIRST AMENDMENT (Secured Reimbursement Agreement)

Exhibit 10.4

FIRST AMENDMENT

(Secured Reimbursement Agreement)

THIS FIRST AMENDMENT dated as of June 22, 2007 (this “Amendment”) amends the secured Amended and Restated Reimbursement Agreement dated as of July 1, 2005 (the “Reimbursement Agreement”) among ACE Limited, a Cayman Islands company (the “Parent”), certain subsidiaries thereof, various lenders and Wachovia Bank, National Association, as Administrative Agent. Capitalized terms used but not defined herein have the respective meanings set forth in the Reimbursement Agreement.

Pursuant to the Parent’s request, the parties have agreed to amend the Reimbursement Agreement to delete the Restricted Payments covenant set forth in Section 5.02(e). Accordingly, the parties hereto agree as follows:

SECTION 1. Amendment to Reimbursement Agreement. Section 5.02(e) is amended in its entirety to read as follows:

(e) [Intentionally Deleted].

SECTION 2. Representations and Warranties. The Parent represents and warrants as follows:

2.1 Authorization. The execution, delivery and performance by the Parent of this Amendment are within its corporate powers, have been duly authorized by all necessary action, and do not: (i) contravene its organizational documents or any contractual restriction, law or governmental regulation or court decree or order that is binding on any Account Party or (iii) require any consent, approval, authorization or other action by, or notice to, or registration or filing with, any governmental authority or other Person.

2.2 Enforceability. This Amendment constitutes the legal, valid and binding obligation of the Parent enforceable against the Parent in accordance with its terms, subject to applicable bankruptcy, insolvency and similar laws affecting creditors’ rights and general equitable principles.

2.3 Representations and Warranties; No Default. After giving effect to this Amendment: (i) each of the representations and warranties of the Account Parties contained in the Reimbursement Agreement (excluding the representation and warranty set forth in Section 4.01(g)) is true and correct on and as of the date hereof with the same effect as if made on and as of the date hereof (except to the extent any such representation or warranty is expressly stated to have been made as of a specific date, in which case such representation or warranty was true and correct as of such date) and (ii) no Default or Event of Default has occurred and is continuing.

SECTION 3. Effectiveness. This Amendment shall become effective as of the date set forth above when the Administrative Agent has received counterparts hereof signed by the Issuing Bank, the Parent and the Required Banks.

SECTION 4. Miscellaneous.

4.1 Effect of Amendment. After the effectiveness hereof, all references to the

Reimbursement Agreement set forth in any other agreement or instrument shall, unless otherwise specifically provided, be references to the Reimbursement Agreement as amended hereby. Except as so amended, the Reimbursement Agreement shall remain in full force and effect in accordance with its terms.

4.2 Governing Law. This Amendment shall be governed by and construed and enforced in accordance with the laws of the State of New York.

4.3 Successors and Assigns. This Amendment shall be binding upon, inure to the benefit of and be enforceable by the respective successors and assigns of the parties hereto.

4.4 Construction. Headings used herein are for convenience of reference only and shall not affect the meaning of this Amendment.

4.5 Counterparts. This Amendment may be executed in any number of counterparts and by different parties hereto on separate counterparts, each of which shall be an original and all of which taken together shall constitute one and the same agreement. Delivery to the Administrative Agent of a signed counterpart hereof, or signature page hereto, by facsimile or e-mail (in a .pdf or similar file) shall be effective as delivery of an original manually-signed counterpart.

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IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be executed by their duly authorized officers as of the date first above written.

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