FACTUAL INFORMATION A Boeing 737 was maintaining FL200 while enroute from Sydney to Canberra via Wollongong and a Beech 1900 was maintaining FL190 while enroute from Cooma to Sydney via Shelleys and Bindook. A Saab 340 was enroute from Sydney to Canberra at FL200 tracking via PAGER and Shelleys. The crews of all three aircraft were operating on the same air traffic control frequency when the crew of the Beech 1900 requested climb to FL200 due to turbulence. The air traffic controller had previously assessed that the Beech 1900 would be a possible restriction for the descent of the Boeing 737 into Canberra. However, when the pilot of the Beech 1900 requested climb to avoid the turbulence, the controller forgot this potential conflict. There was a route limitation of not above FL190 without prior coordination with the northern adjacent sector. The controller subsequently assessed that there were no restrictions for the climb and that the Beech 1900 would pass safely in front of the Saab 340. Consequently, the controller coordinated a clearance for the Beech 1900 to climb to FL200 and instructed the pilot to climb to that level. As the pilot of the Beech 1900 commenced climb to FL200 the horizontal distance between that aircraft and the Boeing 737 was approximately 6 NM. The controller then recognised the potential conflict between the Boeing 737 and the Beech 1900 and immediately instructed the pilot of the latter aircraft to maintain FL190. However, the pilot of the Beech 1900 had already left FL190 on climb and was unable to descend back to the original level before the aircraft reached FL195. The horizontal distance between the Beech 1900 and the Boeing 737 at the time was 3 NM. The required separation was 5 NM horizontally or 1000 ft vertically. The controller instructed the crew of the Boeing 737 to turn left onto a heading of 180 degrees to maintain horizontal separation. However, before turning the aircraft, the crew reported that they had the Beech 1900 in sight. The controller provided an update of the position of the Beech 1900 as the aircraft passed 4 NM abeam. The pilot of the Beech 1900 reported at FL190 and the crew of the Boeing 737 reported turning left onto the radar heading. There was a breakdown in separation. ANALYSIS The controller could offer no reason for not including the Boeing 737 in his considerations. Possibly, he became focused on providing relief from the turbulence for the Beech 1900 to the detriment of his overall control. Also, the need to ensure that coordination with the adjacent sector was completed prior to approving the climb for the Beech 1900 may have diverted his attention. SIGNIFICANT FACTORS The controller forgot the relative positions of the aircraft when he approved the pilot of the Beech 1900 to climb to FL200.