B747 CREW HAS COURSE DEV ON DEGES 1F DEP LEAVING LSZH.

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FO PF OF 3-MAN CREW WITH ALSO 1 JUMPSEATER OF SAME COMPANY AND TYPE RATING. DEPARTED LSZH ON RWY 34; DEGES 1F. AUTOPLT AND LNAV ENGAGED AND ACTIVE AT 500 FT AGL. SHORTLY AFTER DEP; AROUND 2400 FT AGL; ACFT MADE SHARP 90 DEG TURN TO THE L; WHILE THE FMS MAGENTA TRACK STILL SHOWED/DISPLAYED A FORWARD TRACK-CONTINUATION OF RWY CTRLINE EXTENSION. FO EXCLAIMED 'WHAT'S IT DOING?' SINCE THE MAGENTA TRACK DID NOT UPDATE ITSELF WITH NEW CURRENT DIRECTION. AIR SPD WAS AT APPROX 178 KTS TO MAINTAIN SID CLB GRADIENT. NONE OF THE PLTS OFFERED ANY EXPLANATION. CAPT SAID TO KICK IT OFF AUTOPLT AND FLY THE MAGENTA TRACK. AS THE ACFT WAS RETURNED TO THE MAGENTA TRACK; TWR ASKED WHY THE TURN WAS DELAYED. CAPT RESPONDED WITH 'FMS DISCREPANCY.' NOTHING FURTHER WAS SAID. CREW WAS ON A LONG DUTY DAY; TOTALING 19 HRS 15 MINS. THIS WAS THE SECOND LEG. FO HAD ALSO PREVIOUSLY FLOWN FIRST LEG 6 HRS 9 MINS; AND AT REQUEST OF CAPT REMAINED IN SEAT FOR SECOND LEG. FO HAD FLOWN FIRST LEG WITHOUT CREW ROTATION REST. FO WAS ON 30TH DAY OF TRIP AND TOTAL BLOCK HRS OF JUST OVER 111 HRS. ALSO; CAPT WANTED TO MAKE CRITICAL SLOT TIME FOR TKOF TO PREVENT FURTHER DELAYS. I BELIEVE THE RUSH; FATIGUE; AND THIS ARPT BEING A FIRST TIME FOR ALL CREW MEMBERS CONTRIBUTED TO THE DELAY IN RECOGNITION OF WHAT THE FMS TRACKING MAY HAVE BEEN INDICATING.