Approval was given to Melbourne Sector 12 by Sydney ATC for the Nomad to climb clear of the Sydney 230 radial for parachute dropping from FL125. At about the same time, an Airbus was inbound to Sydney from Melbourne via a Rivet STAR. As the Airbus was passing FL130 on descent, the Nomad was observed on radar by Sydney Arrivals, near the inbound track climbing through FL110, in potential conflict with the descending Airbus. The Arrivals Controller contacted Melbourne Sector 12 who confirmed that they would be separating the two aircraft. Although this was accepted, a short time later the aircraft were observed to pass within 4 NM of each other at the same level, when the minimum lateral separation required was 5 NM. A subsequent investigation did not reveal any reason for the lack of positive control by Melbourne Sector 12. The incident was also the subject of a separate ATS Quality Assurance investigation.