EXHIBIT 23.1 CONSENT OF INDEPENDENT ACCOUNTANTS We consent to the incorporation by reference in this Form 8-K dated May 20, 1998, of our report dated February 20, 1998 on our audits of the consolidated financial statements of Greater Bay Bancorp and Subsidiaries as of December 31, 1997 and 1996, and for the three years in the period ended December 31, 1997, appearing in the Annual Report on Form 10-K of Greater Bay Bancorp and Subsidiaries as filed with the SEC on March 31, 1998. /s/ Coopers & Lybrand L.L.P. San Francisco, California May 20, 1998