What was found
AT FL 340, VNAV, LNAV ENGAGED. AUDIBLE CLICK WAS HEARD. ALL NAV DATA REMOVED FROM BOTH NAV DISPLAYS, NO WARNING OR FAULTS DISPLAYED, NO CIRCUIT BREAKER TRIPPED. WITHIN 30 SECONDS CDU MENU PAGE DISPLAYED WITH ABSENCE OF FMC ON MENU. WITHIN NEXT 30 SECONDS BOTH NAVS DISPLAYED NAV DATA FOLLOWED BY FMC RETURNING TO MENU PAGE. FMC SELECTED AND OPS NORMAL. NO QRH CHECKLIST ACCOMPLISHED. ON LANDING "FMC DISAGREE" FAULT ILLUMINATED ON CDU & NAV DISPLAY. ACFT GROUNDED. VERIFIED NO C/B'S POPPED. VERIFIED NO TRAX 30 DAY HISTORY. PERFORMED FIM 34-61, TASK 835. NO CURENT FAULTS FOUND ON FMC 1 OR 2. FOUND FMC FAULTS DURING FLIGHT LEG 1 FOR BOTH FMC'S DURING FMC BITE. PERFORMED FMC SYS OPS CK REF AMM 34-61-00 ON BOTH FMC. NO FAULTS NOTED. NR 1 AND NR 2 FMC'S OPS CHECKED GOOD. ETOPS SIGNIFICANT SYS GROUND VERIFICATION SUCCESSFUL.