The aircraft failed to comply with the Melbourne runway 34 ARBEY 6 STAR tracking instructions at BUNKY. At BUNKY, the aircraft was observed on radar to track to FENTONS HILL instead of tracking to DEERS. The crew, in answer to a query from air traffic control (ATC), confirmed that they were turning at BUNKY but radar indicated that the aircraft failed to execute the turn. Consequently, ATC cancelled the STAR clearance and the crew were instructed by the approach controller to turn right onto a heading of 200 degrees. The crew acknowledged this instruction but failed to execute the turn. The crew finally commenced the turn at Fentons Hill some 10nm after the initial STAR transition point (BUNKY) for Melbourne runway 34. The aircraft was subsequently radar vectored to land on runway 34. It was undetermined as to why the crew did not turn at BUNKY or fully comply with the controller's subsequent instructions. It appears that the crew probably misidentified FENTONS HILL as BUNKY. There was no breakdown in separation.