Lisa B. Peters Senior Executive Vice President

Exhibit 10.3

Lisa B. Peters Senior Executive Vice President

July 10, 2008

Mr. Thomas P. Gibbons

The Bank of New York Mellon Corporation

One Wall Street

New York, New York 10286

Re:    Appointment as Chief Financial Officer

Dear Todd:

This letter relates to your appointment as Chief Financial Officer of BNY-Mellon and the agreement between you and The Bank of New York Company, Inc., dated June 25, 2007 (the “Transition Agreement”). If you agree, this letter will amend the Transition Agreement.

Effective as of July 1, 2008 (the “Effective Date”), you will be appointed Chief Financial Officer of BNY-Mellon. For the avoidance of doubt, your new position and its related reporting requirements shall not of itself constitute Good Reason.

You also agree that, effective as of the Effective Date, you are waiving the provisions of Section 3(b) of the Transition Agreement and that, as of such date, Section 3(b) shall be of no further force and effect.

You agree that Section 4(j) of the Transition Agreement is restated in its entirety to read as follows:

(j) Section 409A of the Code. Notwithstanding anything to the contrary in this Agreement or elsewhere, if you are a “specified employee” as determined pursuant to Section 409A of the Code as of the date of your “separation from service” (within the meaning of Final Treasury Regulation 1.409A-1(h)) and if any payment or benefit provided for in this Agreement or otherwise both (x) constitutes a “deferral of compensation” within the meaning of Section 409A and (y) cannot be paid or provided in the manner otherwise provided without subjecting you to “additional tax”, interest or penalties under Section 409A, then any such payment or benefit that is payable during the first six months following your “separation from service” shall be paid or provided to you in a cash lump-sum on the first business day of the seventh calendar month following the month in which your “separation from service” occurs or, if earlier, at your death. In addition, any payment or benefit due upon a termination of your employment that represents a “deferral of compensation” within the meaning of Section 409A shall only be paid or provided to you upon a “separation

Human Resources

One Wall Street, 10th Floor, New York, NY 10286

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from service”. Notwithstanding anything to the contrary in this Agreement or elsewhere, any payment or benefit under this Agreement or otherwise that is exempt from Section 409A pursuant to Final Treasury Regulation 1.409A-1(b)(9)(v)(A) or (C) shall be paid or provided to you only to the extent that the expenses are not incurred, or the benefits are not provided, beyond the last day of your second taxable year following your taxable year in which the “separation from service” occurs; and provided further that such expenses are reimbursed no later than the last day of your third taxable year following the taxable year in which your “separation from service” occurs. Except as otherwise expressly provided herein, to the extent any reimbursement or in-kind benefit under this Agreement constitutes a deferral of compensation, the amount of any such expenses eligible for reimbursement (or in-kind benefits to be provided) in one calendar year shall not affect the expenses eligible for reimbursement) or in-kind benefits to be provided) in any other taxable year, in no event shall any expenses be reimbursed after the last day of the calendar year following the calendar year in which you incurred such expenses, and in no event shall any right to reimbursement (or in-kind benefit) be subject to liquidation or exchange for another benefit.

The terms of the Transition Agreement not amended herein shall remain in force and are not affected by this letter. This letter will be governed and construed in accordance with the laws of the State of New York, without reference to principles of conflict of laws. For ease of reference, any capitalized terms used but not defined in this letter are used with the same meaning as under the Transition Agreement.

If the terms of this letter are acceptable to you, please sign both copies of this letter indicating your agreement to its terms, keep one signed copy of the letter for yourself and return the other signed copy to me. This letter may be executed in two or more counterparts, each of which will be deemed to be an original. A signature transmitted by facsimile will be deemed an original signature.

Date: 7/16/08