HEADING TRACK DEV IN A DA20 DURING DEP FROM RWY 27R AT PBI; FL. NON ADHERENCE TO ATC CLRNC INSTRUCTION.

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ACFT WAS CLRED TO TAXI TO RWY 27R FOR DEP. AS WE SWITCHED TO TWR FREQ; TWR WAS ALREADY CLRING US FOR TKOF; WE WERE INSTRUCTED TO FLY HDG 275 DEGS (RWY HEADING). IN THE CLB OUT ABOUT 500-1000 FT AGL I BANKED TO A 275 DEG HDG. SHORTLY AFTER DOING SO; ATC (PBI DEP) DIRECTED US TO TURN R TO A 300 DEG HDG. IN THE NEXT FEW XMISSIONS FROM ATC WE WERE ASKED TO TURN FURTHER AND FURTHER R (NW) UNTIL FINALLY; 1 CTLR ASKED US TO VERIFY THAT WE WERE FLYING THE ASSIGNED HDG (330 DEGS). THE CTLR INFORMED US THAT WE APPEARED TO BE CONSISTENTLY TRACKING 20-30 DEGS L (S) OF OUR ASSIGNED COURSE. WE THEN RECHKED OUR HSI'S AGAINST THE 'WET' COMPASS AND FOUND THEM BOTH IN ERROR ABOUT 30 DEGS. WITH THIS ERROR; WHEN THE ACFT WAS BANKED TO 275 DEGS AFTER DEP IT WAS ACTUALLY FLYING ABOUT 245 DEGS. WE THEN CHKED WITH THE INITIAL DEP CTLR TO BE SURE NO CONFLICT HAD OCCURRED DEPARTING PBI. PBI VERIFIED THAT NO CONFLICT HAD OCCURRED AND THAT ACTUALLY OUR DEV FROM COURSE ALLOWED THEM TO GET ANOTHER ACFT DEPARTED EARLIER. UPON RETURNING TO OUR HOME BASE AT TRIP COMPLETION; THE PROB WAS 'SQUAWKED' BUT COULD NOT BE DUPLICATED BY MAINT. IT OCCURRED ONLY 1 ADDITIONAL TIME IN THE REMAINING 4.5 HRS OF FLYING. OUR ACFT COMPANY CHKLIST PROVIDES FOR 2 'RECHKS' OF HEADING-COMPASS DURING TAXI AND PRE-TKOF CHKS AND ALL CHKLISTS HAD BEEN PERFORMED (CHALLENGE AND RESPONSE). INITIALLY; BOTH I AND THE CAPT WERE AFRAID WE HAD DEPARTED THE WRONG RWY AT PBI (RWY 31) ACCIDENTALLY. (WE BOTH REALIZED SOMETHING WAS WRONG WHEN; 1) I HAD TO BANK 30 DEGS TO THE ASSIGNED HEADING -- IF I HAD DEPARTED RWY 27; NO BANK SHOULD HAVE BEEN REQUIRED! 2) WHEN ATC TURNED US BACK TO A 300 DEG HDG ALMOST IMMEDIATELY AFTER DEP.) BUT AFTER REVIEWING THE ARPT MAP AND CONFIRMING WITH EACH OTHER THAT WE HAD PROPERLY COMPLETED APPROPRIATE CHKLISTS; WE KNEW WE HAD DEFINITELY SET OUR HSI'S CORRECTLY PRIOR TO DEP AND HAD INDEED DEPARTED RWY 27R. NEVERTHELESS; BECAUSE THE TKOF WAS RUSHED; (SINCE TWR CLRED US BEFORE WE EVEN CALLED HOLDING SHORT) THERE WAS A MOMENT OF CONFUSION (PANIC!?) WHEN WE FIRST NOTICED SOMETHING WAS 'OFF' WHERE WE QUESTIONED OUR OWN ACTIONS RATHER THAN IMMEDIATELY QUESTIONING THE EQUIP ACCURACY! ALTHOUGH NO CONFLICTS OCCURRED; WE MIGHT HAVE CAUGHT THE PROB QUICKER AND SOLVED IT BEFORE ATC HAD TO BRING IT TO OUR ATTN.