USING A DIFFERENT RWY THAN BRIEFED FOR DEP; A CL604 CREW TURNS THE WRONG WAY AFTER TKOF FROM CLT.

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ARRIVING FROM BERMUDA; WITH NO PAX; A CREW OF 3 PLTS AND A FLT ATTENDANT; WE WERE MAKING A STOP IN CLT TO CLR CUSTOMS. OUR PREFERRED RWY WAS RWY 37R DUE TO THE SHORT TAXI TO FBO. WE DID RECEIVE RWY 36R FOR ARR AND ASSUMED IT TO BE OUR DEP RWY AS WELL; FOR THEY WERE USING RWY 36R FOR DEPS. WHILE THE CAPT WAS CLRING CUSTOMS; I RECEIVED THE CLRNC OUTBOUND WITH THE HELP OF THE RELIEF PLT WITH WHOM I WOULD BE FLYING THIS EMPTY LEG TO AVL. WE RECEIVED THE HORNET 1 DEP WHICH STATES; AFTER DEPARTING OFF RWY 36R AT THE 2.5 DME TURN R TO A HDG OF 025 DEGS THEN EXPECT RADAR VECTORS. THIS WAS BRIEFED BTWN MYSELF (THE PF) AND THE PNF. WE CONTACTED GND CTL; WHICH DIRECTED US TO RWY 36L. WE TOLD HIM THAT WE ARE REQUESTING RWY 36R DUE TO THE SHORTER TAXI. HIS REPLY WAS THE TAXI MAY BE SHORTER; BUT THE WAIT TIME WOULD BE LONGER DUE TO OUR DIRECTION OF FLT. WE THEN ACCEPTED THE TAXI CLRNC TO RWY 36L. AFTER DEP OFF RWY 36L AT THE 2.5 DME; WE TURNED R TO A HDG OF 025 DEGS; JUST AS WE HAD BRIEFED. HOWEVER; THE DEP PROC FOR RWY 36L CALLED FOR A L TURN TO 330 DEGS. CONTACT WITH DEP WAS NORMAL AND WE WERE GIVEN A RADAR VECTOR TOWARD OUR DEST. NOTHING WAS MENTIONED TO US BY DEP CTL ABOUT THE TURN.