C650 CREW HAD READBACK; HEARBACK CONFUSION WITH ATC.

Narrative

SHORTLY AFTER OUR TKOF FROM ILG; PHILADELPHIA DEP CTL CLRED US TO CLB TO 5000 FT. WE WERE TURNING TO AN ASSIGNED 330 DEG HDG. A MOMENT LATER PHILADELPHIA DEP CTL ISSUED US; ANOTHER CLRNC TO PROCEED DIRECT TO THE OOD VOR WHEN CLBING OUT OF 2000 FT. I READ BACK 'DIRECT OOD LEAVING 2000 FT.' WHEN WE REACHED 2000 FT IN OUR CLB TO 5000 FT WE STARTED A R TURN (THE SHORTEST TURN) TOWARD OOD. DURING THIS TURN WE RECEIVED ANOTHER RADIO XMISSION FROM PHILADELPHIA DEP CTL; ASKING US WHICH WAY WE WERE TURNING. I REPLIED 'TO THE R.' THE CTLR THEN STATED HE HAD ISSUED US INSTRUCTION TO TURN 'L' DIRECT OOD. MY FO AND MYSELF HAVE NO MEMORY OF HIS TELLING US TO TURN EITHER L OR R BUT ONLY TO PROCEED DIRECT OOD LEAVING 2000 FT. WE WERE CONDUCTING THE AFTER TKOF CHKLIST WHEN HE CALLED AND IT'S POSSIBLE WE MISSED IT; BUT IT'S ALSO POSSIBLE HE DID NOT SPECIFY A L OR R TURN; WE JUST DON'T KNOW FOR SURE. BUT WE ARE SURE I DID NOT READ BACK A DIRECTION OF TURN. THERE WAS NO FURTHER XMISSIONS REGARDING THIS MATTER FROM ATC AND NO FURTHER CHANGES IN HEADING OR ALT AND TO THE BEST OF OUR KNOWLEDGE IT DID NOT RESULT IN A HAZARDOUS SIT. IF WE MISSED PART OF THE CLRNC IT MEANS WE NEED TO LISTEN MORE CLOSELY; ESPECIALLY WHEN CONDUCTING CHKLISTS AND WE HAVE MADE A COMMITMENT TO DO THAT AS COCKPIT PROC. THIS IS A GOOD IDEA NO MATTER WHERE THE ERROR WAS IN THIS PARTICULAR MATTER.