What was found
ATC CLEARED US DIRECT TILLT. BOTH CDU'S SHOWED DIRECT TILLT, BUT THE FO MAP DISPLAY STILL SHOWED THE PREVIOUS WAYPOINT, RBL, AND LNAV WAS STILL PROCEEDING DIR. RBL WITH AUTOPILOT B ENGAGED. THIS PERSISTED FOR APPROX 1 MIN, THEN THE FO MAP SYNCED UP AND THINGS SEEMED NORMAL A FEW MINUTES LATER THE RIGHT FMC FAILED. THIS PERSISTED FOR APPROX 1 MIN AND SEEMED TO NORMALIZE. GROUNDED - YES. ACCOMPLISHED FMC BITE PER B737-900 FIM 34-61 TASK 801, LOGGED PGM FAULT FOR R FMC. ACCOMPLISHED FIM 34-61 TASK 807, R FMC OPS NML.