Exhibit 32.1

Certification

Pursuant to the requirement set forth in Section 906 of the Sarbanes-Oxley Act of 2002 Byron A. Scordelis hereby certifies as follows:

1. He is the duly appointed Chief Executive Officer of Greater Bay Bancorp, a California corporation (the “Company”).

2. Based on his knowledge, the Company’s Quarterly Report on Form 10-Q for the period ended September 30, 2006, and to which this Certification is attached as Exhibit 32.1 (the “Periodic Report”), fully complies with the requirements of section 13(a) or section 15(d) of the Securities Exchange Act of 1934 and the information contained in the Periodic Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

IN WITNESS WHEREOF, the undersigned has set his hand hereto as of this 9^th day of November, 2006.

/s/ BYRON A. SCORDELIS

Byron A. Scordelis

Chief Executive Officer