What was found
AIRCRAFT IN FLIGHT AT HIGH ALTITUDE (FL410) AIRCRAFT GOT SLOW (APPROXIMATELY 165 KNOTS). RIGHT ENGINE FLAMED OUT. ADVISE ATC THAT WE HAD ENGINE PROBLEM AND REQUEST TO GO DOWN TO FL270 TO RESTART ENGINE. DESCENDED TO FL270 AND RESTARTED ENGINE. NO OTHER ABNORMALITIES OCCURRED DURING BALANCE OF FLIGHT. AFTER AIRCRAFT RETURNED. ENGINE WAS INSPECTED IN INLET, EXHAUST AND ACCESSORY SECTIONS, NO FAULTS FOUND. ENGINE WAS GROUND PERFORMANCE RAN WITH NO FAULTS FOUND. OK FOR RETURN TO SERVICE. NOTE: AN ALTITUDE ACCELERATION TEST WAS PERFORMED ON THIS AIRCRAFT ON 02/27/2003 AND THE RIGHT ENGINE FLAMED OUT AT FL370. AIRCRAFT WAS RESTRICTED TO FL350.