Exhibit (32)(b)

Certification pursuant to 18 U.S.C. Section 1350,

as adopted pursuant to Section 906 of the Sarbanes-OxleyAct of 2002

In connection with the Form 10-Q of The First American Corporation (the “Company”) for the period ended June 30, 2003, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Thomas A. Klemens, Chief Financial Officer of the Company, certify, pursuant to 18 U.S.C. §1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that:

1) the Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended; and

2) the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

/s/    THOMAS A. KLEMENS        

Thomas A. Klemens

Chief Financial Officer

November 14, 2003