Hudson 587 [HS748] was proceeding on a flight from East Sale to East Sale via Dubbo at Flight Level [FL] 170. While under the control of Melbourne Sector 2 the pilot requested a climb to FL190 and a diversion east of track for weather avoidance. The request was approved by air traffic control who then co-ordinated the changes with Sydney Flight Information Service [FIS] 6 as the track would take the aircraft outside controlled airspace [OCTA] for 8nm before entering Sydney Sector 6 airspace. Some confusion arose as to which FIS position was responsible for the airspace because officers were still unfamiliar with recent boundary changes. The FIS 6 position was the wrong position to which to direct the co-ordination as FIS 2 had responsibility for that portion of airspace. The FIS 6 operator misjudged the actual track of Hudson 587 believing that the aircraft would remain in controlled airspace and, as such, the Melbourne Sector 2 controller would co-ordinate directly with the Sydney Sector 6 controller. On that basis the FIS 6 operator decided that no further action by him was required. The Melbourne Sector 2 controller, although co-ordinating with the wrong FIS, instructed Hudson 587 to call Sydney on the correct frequency, which the crew did. The FIS 2 operator heard the call but was not expecting the aircraft as no co-ordination had been received by him. He immediately commenced co-ordination checks with Melbourne Sector 2, FIS 6 and Sydney Sector 6 to establish the current status of Hudson 587. Finally, Sydney Sector 6 issued an airways clearance for Hudson 587, but, as the aircraft was only OCTA for approximately three minutes, the clearance was not issued in time to prevent Hudson 587 penetrating controlled airspace without a clearance. Significant Factors 1. The co-ordination procedures for the revised airspace boundaries were not adequately documented. 2. The Melbourne Sector 2 controller co-ordinated with the wrong FIS operator. 3. The FIS 6 operator miscalculated the track of Hudson 587. 4. The FIS 6 operator did not co-ordinate the position of Hudson 587 after accepting the report from Melbourne Sector 2. 5. There was no breakdown in separation.