FO OF AN LTT TURBOPROP STARTED TURNING AFTER TKOF IN THE OPPOSITE DIRECTION THAN ASSIGNED BY TWR. THE CAPT AND TWR CTLR REMINDED THE FO TO TURN THE OTHER WAY WHICH HE SUBSEQUENTLY DID WITHOUT FURTHER CONFLICT.

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TAKING OFF ON RWY 32; WE WERE CLRED FOR A R TURN ON COURSE. A CESSNA WAS ON R DOWNWIND FOR RWY 14. AS WE CLBED; THE PF BEGAN A TURN TO THE L; TOWARDS THE CESSNA PARALLELING US. I SAID NO; R TURN. THE PF STOPPED THE BANK; BUT DID NOT BEGIN A R TURN. BOTH I AND THE CTLR EXCLAIMED 'R TURN;' AND WE STARTED A R TURN AND DEPARTED THE PATTERN. THE TCASII SHOWED 700 FT OF VERT SEPARATION; AND I AM NOT CERTAIN OF THE HORIZ DISTANCE. I DID NOT CONSIDER IT A NEAR MISS; BUT HAD WE CONTINUED ON OUR COURSE IT WOULD HAVE BEEN. I AM NOT CERTAIN WHAT CAUSED THE PF'S CONFUSION; BUT I SPECULATE THAT THE FACT THAT WE HAD LANDED OPPOSITE DIRECTION ON RWY 14; AND FATIGUE FROM A LONG SCHEDULE MAY HAVE CONTRIBUTED. MY ROLE AS PIC IS TO ENSURE THAT THIS DOESN'T HAPPEN. I TYPICALLY VERBALIZE THE CLRNC AS WE TAKE THE RWY; AND IN THIS CIRCUMSTANCE; I DON'T REMEMBER IF I RE-EMPHASIZED THE R TURN. PERSONALLY; I WAS FATIGUED AT THE END OF A LONG WK; ON MY 4TH DAY OF 11-13 HRS OF DUTY PER DAY. I WAS ALSO LESS ALERT DUE TO THE HIGH EXPERIENCE OF THE FO; AND VFR WX. IF I COULD DO IT AGAIN; I WOULD CLRLY AND STRONGLY VERBALIZE THE TKOF CLRNC AFTER THE FO'S READBACK; AND WOULD TAKE THE CTLS TO BANK THE AIRPLANE R INSTEAD OF TELLING THE FO TO DO SO WHEN THERE MIGHT BE A TFC CONFLICT. I ALSO NEED TO TREAT EVERY TKOF AS CRITICAL; EVEN AT THE END OF A LONG WK. THIS ONE GOT AWAY FROM ME.