PLT OF A PIPER CHEYENNE TURNED TO THE HDG OF 035 DEGS AFTER TKOF; AS RECORDED DURING CLRNC DELIVERY; AND WAS SUBSEQUENTLY ADVISED BY DEP CTLR THAT THE ASSIGNED HDG WAS REALLY 350 DEGS.

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AFTER LISTENING TO ATIS; RECEIVING MY CLRNC TO PIR; AND TAXIING TO RWY 11L; I COMPLETED THE CHKLIST AND DID A RUNUP AND SYS CHK. I CALLED TWR FOR TKOF AND WAS ADVISED TO TURN L TO 035 DEGS IMMEDIATELY AFTER TKOF. I WROTE DOWN 035 DEGS ON MY NOTE PAD AND DIALED IN 035 DEGS ON THE HSI. AFTER TKOF; I WAS ADVISED AGAIN TO DO THE IMMEDIATE L TURN AND TO CONTACT DEP ON 126.1. I TURNED L TO 035 DEGS AND CLBED TO MY ASSIGNED ALT OF 8000 FT. THE DEP FREQ WAS BUSY; SO I MAINTAINED THE 035 DEG HDG AND CLBED TO MY ASSIGNED ALT OF 8000 FT AND WAITED FOR A BREAK TO CALL DEP. AFTER THE INITIAL CALL TO DEP THAT WAS BLOCKED; DEP CALLED ME AND WAS NOT RECEIVING MY XPONDER. I SWITCHED TO THE SECOND XPONDER; WHICH DEP RECEIVED. AT THAT TIME; I WAS TOLD THAT I SHOULD HAVE BEEN ON A 350 DEG HDG AND TO TURN TO 300 DEGS. I MADE THE TURN TO 300 DEGS AND THEN WAS VECTORED TO INTERCEPT AND COMPLETE THE YELLOWSTONE 1 DEP/SCOTTSBLUFF TRANSITION; DIRECT PIR. AFTER THE CALL FROM DEP; I DOUBLECHKED MY NOTES. I ALSO HAD A PVT PLT WITH ME IN THE R SEAT WHO HAD A HEADSET ON AND HAD LISTENED TO ALL COM. I ASKED HIM IF I HAD MADE A MISTAKE ON HEARING OR WRITING DOWN THE CLRNC. HE INDICATED HE ALSO HEARD 035 DEGS ON THE HDG CLRNC. TO MY KNOWLEDGE THERE WASN'T A PROB WITH ANY TFC OR AIRSPACE INCURSIONS. ALSO; THE DEP CTLR WAS VERY ACCOMMODATING AND DID NOT INDICATE ANY PROBS. THIS OCCURRENCE TROUBLED ME AS I TAKE MY FLYING AND SAFETY VERY SERIOUSLY. I TAKE RECURRENT TRAINING (FLT SAFETY) AND AM COMPLETING MY 25TH YR OF ACCIDENT/INCIDENT FREE FLYING.