AMENDMENT 2003A TO GREATER BAY BANCORP 1997 ELECTIVE DEFERRED COMPENSATION PLAN

Exhibit 10.13(b)

AMENDMENT 2003A TO

GREATER BAY BANCORP

1997 ELECTIVE

DEFERRED COMPENSATION PLAN

THIS AMENDMENT TO THE GREATER BAY BANCORP 1997 ELECTIVE DEFERRED COMPENSATION PLAN (this “Amendment”) is made effective as of July 1, 2003, and is made pursuant to the following recitals:

A. Greater Bay Bancorp, a California corporation (the “Company”) adopted the Greater Bay Bancorp 1997 Elective Deferred Compensation Plan (the “Plan”) on November 19, 1997, which Plan subsequently has been amended. Terms used in this Amendment have the same meanings as in the Plan.

B. Section 8.01 of the Plan provides for the amendment of the Plan by the Company.

C. Questions have arisen regarding the crediting of Additions to Participants’ Accounts under the Plan, and the Company has determined that it is in the best interests of the Company and the Subsidiaries to clarify such provisions of the Plan, as set forth in this Amendment, to provide for crediting of such Additions in a manner that is more favorable to Participants than may be currently provided in the Plan.

D. The Company has determined that it is in the best interests of the Company and the Subsidiaries to apply this Amendment to Participants’ Accounts existing on the effective date of this Amendment retroactively to the inception of such Accounts.

NOW, THEREFORE, the Plan is amended as follows:

1. Section 4.03 of the Plan is amended in its entirety to read as follows:

Section 4.03 Crediting of Additions. The Deferred Compensation Contributions that a Participant makes to the Plan each Plan Year shall be deemed to have been invested and reinvested from time to time at the Interest Reference Rate. The Committee shall credit the Participant’s Account with Additions on the Deferred Compensation Contributions credited to the Participant’s Account. Additions to the Participant’s Account shall accrue beginning on the date the Account first has a positive balance and shall continue until the Participant or his or her Beneficiary has received payment of his or her Account in full as provided under Section 5.02. Additions shall be credited quarterly and compounded quarterly to a Participant’s Account. If a Deferred Compensation Contribution is credited to a Participant’s Account during a calendar quarter, the Additions on such Deferred Compensation Contribution for the calendar quarter so credited shall be a prorated amount that is a fraction of the what such

Additions would be for a full calendar quarter; the numerator of the fraction is the number of days in the calendar quarter after the Deferred Compensation Contribution was so credited, and the denominator of the fraction is the total number of days in the calendar quarter. If a payment to a Participant or Beneficiary is made from a Participant’s Account during a calendar quarter, the Additions on the amount so paid for the calendar quarter in which the payment occurs shall be a prorated amount that is a fraction of the what such Additions would be for a full calendar quarter; the numerator of the fraction is the number of days in the calendar quarter prior to the date of payment, and the denominator of the fraction is the total number of days in the calendar quarter.

2. Any corporation that hereafter becomes a Subsidiary and that adopts the Plan in accordance with Section 9.12 of the Plan shall automatically be deemed to have adopted this Amendment as part of the Plan.

3. Except as set forth herein, the Plan shall remain in full force and effect.

IN WITNESS WHEREOF, the Company has caused this Amendment to be executed by its duly authorized officer on the date set forth below, but to be effective as indicated herein.