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The plane was found by a Christchurch-based rescue helicopter this afternoon.
The Rescue Coordination Centre (RCCNZ) had launched a search for the missing aircraft, which took off from Franz Josef about 9am bound for Rangiora in Canterbury, after it was reported overdue by Air Traffic Control at 11am.
One person was on board, the rescue centre said.
Due to poor weather, it was currently too dangerous to get to Mt Nicholson, located in the Froude Range of the Southern Alps.
RCCNZ is coordinating with partner agencies on next steps for the response.
The fate of the pilot is not yet known.