B767-300 FLT CREW PROGRAMS THE FMC INCORRECTLY AND DEVIATES FROM ASSIGNED CLRNC.

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ON A FLT TO ATL; WE WERE GIVEN AN ATC RERTE OFF OUR FILED RTE DIRECT TO CVIKK. I AM A LINE CHK PLT AND I HAD A CAPT STUDENT IN THE L SEAT. THE STUDENT PROGRAMMED THE FMS WITH THE NEW RTE AND WE BOTH CONFIRMED IT AND WENT ON OUR WAY. SOME TIME LATER IN THE FLT THE STUDENT ADDED OUR COMPANY POS RPT POINTS (USING ABEAM POINTS DETERMINED BY THE FMS) TO OUR PROGRAMMED RTE. THE LAST COMPANY RPT POINT WAS BHF; WHICH IS RIGHT NEXT TO CVIKK. THE STUDENT ADDED THE POINT PRIOR TO CVIKK WHEN IT WAS ACTUALLY JUST ON THE OTHER SIDE OF CVIKK. I WAS BUSY PREPARING TO START SOME ENRTE INSTRUCTION AND DID NOT NOTICE THESE CHANGES. OUR FMS RTE WAS NOW TO FLY TO A POINT ABEAM BHF AND THEN GO TO CVIKK (WHICH WOULD THEN BE BEHIND US) AND ON TOWARD ATL. UNFORTUNATELY; THE POINTS WERE SO CLOSE TOGETHER THAT THIS WASN'T AT ALL OBVIOUS BY LOOKING AT THE MAP DISPLAY. WHEN WE CROSSED OVER THE COMPANY RPT POINT ABEAM BHF THE PLANE BEGAN A TURN. I WAS BUSY GOING OVER OUR LESSON TOPIC BUT NOTICED THE TURN AND GLANCED DOWN TO THE MAP DISPLAY; SAW WE WERE OVER WHAT I THOUGHT WAS CVIKK; ASSUMED WE WERE MAKING A SMALL TURN ON COURSE; AND WENT RIGHT BACK TO MY INSTRUCTION. SHORTLY AFTER; MY STUDENT RECOGNIZED WE WERE STILL IN A TURN STATING; 'HEY; WHERE IS THIS THING GOING!?' REALIZING SOMETHING WAS WRONG; BUT; HAVING NO IDEA WHAT; WE BEGAN A TURN BACK TO OUR PLANNED COURSE AND SHORTLY AFTER ZMA CALLED TO FIND OUT WHAT WAS WRONG. I ADVISED WE WERE HAVING A GLITCH WITH THE AUTOFLT SYS AND WERE CORRECTING BACK TO COURSE. MY STUDENT DETERMINED WHAT HAD HAPPENED AFTER A FEW MINS. I STILL HAD NO CLUE -- AND WE CONTINUED ON TO ATL. NO TFC CONFLICT WAS RPTED.