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Chairman John Palmer said by staying on until the end of the year, Fyfe was honouring a commitment he made when he took the top job in 2005.
Palmer gave no reason for Fyfe's departure, saying only "that as a world class chief executive officer Rob wants to continue to challenge himself and explore new opportunities".
"He has ensured that Air New Zealand has remained profitable despite the backdrop of turbulent economic times that have seen airlines lose billions globally," Palmer said in a statement.
Palmer said no deadline had been set to find Fyfe's successor but such appointments typically took about six months.
"We would expect significant international interest in the role and believe there are some very strong candidates from within Air New Zealand's existing executive management team," he said.
Media speculation in New Zealand has suggested Fyfe could move to a British carrier or take the top job at the country's largest telecoms carrier Telecom Corp., where he worked in the 1990s.
Air New Zealand announced a 45 per cent slump in annual earnings in August, as high fuel prices and natural disasters in Christchurch and Japan contributed to what Fyfe described as the most difficult conditions in a decade.
Fyfe's departure comes amid government plans to sell down its existing 77 per cent stake in Air New Zealand to just over 50 per cent during its current term to help rein in a budget deficit.