VH-HYG, an Airbus A320, was en route from Sydney to Perth at flight level (FL) 350. VH-TAG, a Boeing 737, was en route from Adelaide to Perth on the same route and was maintaining FL330. The aircraft position reports for FILET, a reporting point over the Great Australian Bight, revealed that there was a 6 minute interval between the aircraft with HYG in front. The crew of TAG requested approval to climb to FL350. The controller believed that the groundspeed of the aircraft over a 6 minute period would provide the necessary 30 NM longitudinal separation standard and instructed the crew to climb to FL350. The controller requested both crews to report their distance from FLAKE, the reporting point west of FILET. The reports from the crews revealed that the distance between the aircraft was 16 NM. The required separation was either 30 NM or 2,000 ft vertically. There was a breakdown of separation standards. Subsequently, the controller instructed the crew of TAG to descend to FL330 to maintain separation. Controllers were required to check for distance standard between aircraft that had less than 10 minutes between their respective estimates. There was a considerable number of aircraft being managed by the controller at the time of the occurrence. Following the occurrence the controller was replaced at the position. However, prior to the occurrence the controller had approved the crew of VH-HYE, an Airbus A320 en route from Perth to Adelaide, to climb from FL370 to FL390 but had not coordinated this change of level with the next control position. Additionally, the controller had not annotated the new level on the HYE flight progress strip for HYDRA. This flight progress strip would be used to coordinate the position of HYE with the next control position. A second handover/takeover was then conducted with a third controller assuming responsibility for the position. The crew of HYE reported at both the HITCH and HOLLA positions at FL390 while this controller was operating the position. The controller advised Adelaide Sector 4 of HYE's HYDRA estimate and level from the flight progress strips for that position. The crew of HYE reported to Adelaide Sector 4 at HYDRA at FL390. The level was confirmed by Sector 4 from the radar display label. The investigation established that the first controller may have been distracted by aircraft radio transmissions and coordination calls from other control positions while he was endeavouring to annotate all flight progress strips for HYE with the new level. Consequently, he did not annotate the new level, of FL390, in the HYDRA flight progress strip. In relation to TAG, the investigation did not establish the reason for the controller not complying with the requirement to check the distance between aircraft. In both handover/takeovers it is probable that the on-coming controllers did not conduct an adequate review of the flight progress strips. To some degree they may have been limited in their ability to conduct a check of the FPSs because of the level and complexity of the traffic situation. This aspect may also be the reason for the third controller not establishing the difference between the levels provided in the two position reports and that annotated on the HYDRA flight progress strip which was subsequently used for the coordination with Adelaide.