EXHIBIT 23
                  CUPERTINO NATIONAL BANCORP AND SUBSIDIARIES
                       CONSENT OF INDEPENDENT ACCOUNTANTS


     We consent to the incorporation by reference in this Form 8-K and the
Registration Statement on Form S-8 (No. 333-16987) of Greater Bay Bancorp
(formerly Mid-Peninsula Bancorp) of our report dated January 26, 1996, with
respect to the consolidated financial statements of Cupertino National Bancorp
incorporated by reference in its Annual Report on Form 10-K for the year ended
December 31, 1995 filed with the Securities and Exchange Commission.



/s/ Coopers & Lybrand, LLP
- --------------------------

San Francisco, California
March 6, 1997