Four high capacity air transport passenger aircraft were en route to Perth under the control of the Melbourne Sector 1 controller, using procedural control methods. Two aircraft were on air route L513 and the other two aircraft were on air route Q76/J68. The routes converged and aircraft at the same level or not longitudinally separated would be in lateral conflict at the Perth 150 NM position for the routes. The aircraft were occupying FL270, FL280 and FL290. Aircraft on the same routes were separated by the minimum vertical separation standard of 1,000 ft. However, the aircraft's estimates for the 150 NM Perth positions were within an eight minute period which did not provide a longitudinal separation standard. The controller elected to descend VH-TAX, a Boeing 737, which was at FL280 on route Q76/J68 to FL260 prior to the 150 NM position, to maintain separation with an aircraft at the same level on route L513. The crew descended to FL260 as instructed. Subsequently, the sector 1 controller was queried by another controller as to the separation standard used to maintain separation with VH-HYJ, an Airbus A320, which was on route Q76/J68 at FL270. The controller had descended TAX through the level of HYJ without an appropriate longitudinal standard being applied between the aircraft. There was a breakdown of separation. The lack of a logitudinal standard between TAX and HYJ had been recognised by the previous sector controller. This controller had annotated the flight progress strips for HYJ to provide a prompt for distance checks. The sector 1 controller was nearing the end of his shift, during which he had worked the last three hours alone. To accommodate training commitments for other controllers and for his own purposes the controller's shifts had been swapped on a number of occasions. The number of recent shifts worked, the time of day and the fact that the controller was nearing the end of his shift probably combined to provide an environment in which he became less vigilant in the scanning of the flight progress strips. Consequently, he did not appreciate that there was not a longitudinal separation standard between the aircraft.