The Boeing 737 (B737) was maintaining flight level (FL) 350 and the Melbourne Central controller had completed all the required tasks involving that aircraft. Although the aircraft had not yet reached the point at which it would normally be handed off to the next sector (Sector 4), the controller decided to proceed with an early hand-off which was accepted by the Sector 4 controller. The Airbus A320 was maintaining FL370 on a track which crossed that of the B737. The appropriate vertical separation standard of 2,000 ft was being maintained. As the tracks of the aircraft converged, the crew of the A320 was given descent to FL350 by the Melbourne Central controller, who momentarily forgot about the B737. As soon as the crew of the A320 reported leaving FL370, the controller realised that he could not guarantee the required horizontal separation standard of 5 NM and immediately instructed them to return to FL370. The A320 had descended to FL368 before the crew were able to arrest the descent and commence climb back to FL370 and re-establish a vertical separation standard. The investigation revealed that the aircraft were at the same flight level, with a horizontal separation of 4.7 NM, resulting in a breakdown of separation standards. The practice of early hand-off is being reviewed by Airservices Australia as it can lead to a reduced level of awareness by controllers.