BE40 FLC TURN ONTO CLRED RTE WHICH CONFLICTS WITH ANOTHER ACFT DUE TO INCOMPLETE ZNY CLRNC.

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THE CREW RECEIVED THE CLRNC FROM JFK CLRNC DELIVERY. WAS CLRED TO LEX VIA KENNEDY 9 DEP; INTERCEPT THE JFK 185 DEG RADIAL; RBV AS FILED (CYN; J37 GVE DIRECT LEX). 5000 FT EXPECT FL350 IN 10 MINS. READBACK WAS VERIFIED AS CORRECT BY JFK CLRNC DELIVERY. ACFT WAS CLRED FOR TKOF AND EVENTUALLY CLRED TO 17000 FT AND DIRECT RBV. AUTOPLT WAS ENGAGED AND IN NAV MODE. OVER RBV; THE FLT DIRECTOR TURNED THE ACFT TOWARDS THE NEXT WAYPOINT; CYN VOR. THIS TURN CREATED A CONFLICT AND ATC COMMANDED A TURN TO 270 DEGS; THEN TO 360 DEGS. ATC HAD ISSUED A CLB TO FL220 JUST AS ACFT APCHED RBV. ATC ASKED CREW IF THEY MISUNDERSTOOD THE CLB CLRNC TO FL220; AND INSTEAD TURNED TO A HEADING OF 220 DEGS. CREW REPLIED THAT THE TURN TO CYN WAS THE ISSUED CLRNC AND THAT THE CREW UNDERSTOOD '220' WAS A CLB CLRNC. CREW QUERIED ATC AND ASKED THEM WHAT CLRNC ATC SHOWED FOR US. ATC STATED THE CLRNC THEY SHOWED WAS RBV J230 J6 HVQ DIRECT. (J230 IS ALIGNED WITH THE RBV 275 DEG RADIAL). CREW REQUESTED ATC PHONE NUMBER AND WAS INFORMED BY ATC THE AUDIO TAPES WOULD BE REVIEWED FROM JFK CLRNC DELIVERY. THE TAPES REVEALED THE CREW WAS FOLLOWING THE RTE ASSIGNED BY ATC AND THAT NO REVISED CLRNC HAD BEEN ISSUED TO THE FLT CREW.