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