HS-TGC operating as flight TG484 took off from runway 34 on initial climb to flight level 280. At 1518 hours local, following reports from members of the public, Sydney Air Traffic Control advised the crew that an object had been seen to fall from the aircraft shortly after take-off. The captain requested further information before a decision was taken whether to continue the flight or return to Sydney. At 1622 hours the aircraft was transferred to an Adelaide ATC frequency and at 1658 hours a report was passed from the company which provided engineering support to the airline in Sydney. The report indicated two pieces of metal were recovered. They were 30 cm and 45 cm in length and were pieces of an exhaust nozzle although the engine which lost the pieces could not be identified. A recommendation was passed to the captain to monitor all engine indications and if no abnormality were evident, it would be safe to continue to the destination. The captain advised that all engine indications were normal and that the flight would continue as planned. The aircraft landed safely at its destination. After arrival, the long fixed core exhaust nozzle (LFCEN) from number three engine was found to be missing. Subsequently, eight pieces of the exhaust nozzle were recovered in an area approximately 2.4-4.9 km beyond the northern end of runway 34. There were no injuries to persons under the flight path and property damage was minimal. A technical investigation revealed that material failure caused the separation of the LFCEN from the engine body. The attachment fitting which secures the LFCEN to the engine body failed as a result of extensive fatigue cracking. A service bulletin was issued by the engine manufacturer in February 1987 which recommended fitment of secondary attachment hardware for the LFCEN. As an alternative, it was recommended the primary attachment fittings be inspected on a regular basis (every 750 engine cycles) for cracking. The airline complied with the alternative recommendation but with an extension of the time between inspections to every 1,000 cycles. No. 3 engine had completed 666 cycles at the time of failure. In-flight separation of an LFCEN from the type of engine fitted to HS-TGC is an extremely rare event. The engine manufacturer has notified all affected aircraft operators of the circumstances and findings. The manufacturer also renewed its recommendations contained in the service bulletin which advocated the fitting of secondary attachment hardware to the LFCEN. The airline has taken action to ensure a fleet-wide inspection of all LFCEN attachment fittings at the next 'A' aircraft check and fitment of secondary attachment hardware in accordance with the engine manufacturer's service bulletin.