ADDENDUM TO CONSULTING AGREEMENT AND CONFIDENTIAL SEPARATION AGREEMENT AND GENERAL RELEASE OF CLAIMS

Exhibit 10.6(c)

ADDENDUM TO CONSULTING AGREEMENT AND

CONFIDENTIAL SEPARATION AGREEMENT

AND GENERAL RELEASE OF CLAIMS

This Addendum is made to that certain Consulting Agreement, dated as of September 29, 2003, by and between Greater Bay Bancorp (the “Company”) and Steven C. Smith (“Mr. Smith”) (the “Consulting Agreement”), and that certain Confidential Separation Agreement and General Release of Claims, dated as of September 29, 2003, by and between the Company and Mr. Smith (the “Separation Agreement” and, together with the Consulting Agreement, the “Agreements”).

WHEREAS, the Agreements provide that Mr. Smith will continue in his current positions with the Company until 30 days after the Company hires a replacement chief financial officer, but in no event later than December 31, 2003;

WHEREAS, the Company has requested Mr. Smith to remain in his current positions for a period of time after December 31, 2003 while the Company continues its search for a new chief financial officer, and Mr. Smith has agreed to do so;

NOW, THEREFORE, in consideration of the foregoing, the parties hereto agree as follows:

1. This Addendum hereby amends the Separation Agreement and the Consulting Agreement to revise the second sentence of Section 1 of the Separation Agreement to read as follows: “Smith agrees to continue in his employment with the Company until 30 days after the Company hires a replacement chief financial officer, but in no event later than February 29, 2004, unless the Company and Smith agree to continue his employment for successive 60 day periods thereafter.” The date specified in the preceding sentence shall be referred to as the “Retirement Date” and shall be substituted for the definition of such term as used in the Separation Agreement and the Consulting Agreement. Accordingly, the Company and Mr. Smith agree that Mr. Smith will continue in his current positions as Executive Vice President and Chief Financial Officer and all other positions he holds with the Company and its subsidiaries until the Retirement Date and the Consulting Agreement will commence on the day after the Retirement Date.

2. The Company agrees that Mr. Smith will be considered for a pro rated bonus for the period of time that he is employed by the Company in 2004. Such bonus will be in the discretion of the Compensation Committee of the Company’s Board of Directors and will take into account the performance of Mr. Smith and the Company during that period.

3. Except as amended hereby, the remaining terms of the Separation Agreement and the Consulting Agreement shall remain in full force and effect.

IN WITNESS WHEREOF, the parties have executed this Addendum as of December 18, 2003.