While taxiing VH-WZJ was advised by Flight Service that traffic was VH-LHF which had taxied at Mildura nine minutes earlier for Essendon. VH-WZJ gave three radio calls on the MTAF frequency but received no response. VH-WZJ departed from runway 09 and at 600 feet above ground level turned to set a heading for Melbourne. As the turn commenced, VH-LHF asked if he had been sighted. VH-LHF was directly ahead but high at 3000 feet. VH-LHF had departed from runway 36 and turned right across the centreline of runway 09. The captain of VH-WZJ complained that had he received an earlier response from VH-LHF he would have arranged his departure flight profile for more appropriate separation. The pilot-in-command of VH-LHF had with him a commercial pilot as a backup safety pilot. Neither of them recalls the three radio calls made by VH-WZJ while taxiing. However, they both had VH-WZJ sighted throughout the alleged incident. The pilots in VH-LHF purposely remained well clear of VH-WZJ. There was no breakdown in separation.