The crew of PAL210 transferred from Melbourne Control (Sector 6) to Brisbane Control (Sector 5) at 1523 hours. On first contact with Brisbane Control they advised an estimate of 1527 hours for Cunnamulla. The Brisbane controller had not received co-ordination from Melbourne Sector 6 on the prior position of the aircraft. He only held an estimate based on the departure time and the flight plan time intervals. That estimate was 1534 hours. Investigation revealed a breakdown had occurred at Melbourne Sector 6, the control position responsible for the co-ordination. This had happened at the time of hand over of responsibilities at the end of a shift. The controller going off duty indicated to the controller coming on duty the need for co-ordination in respect of PAL210 but the manner in which he did this was misinterpreted by the on-coming controller and the required co-ordination was not done. Significant Factor The following factor was considered relevant to the development of the incident: 1. A misunderstanding occurred between the controller going off duty and the controller coming on duty.