Two bodies have been discovered on the Tasman Glacier from two separate historical climbing incidents.
The police had already sent away DNA samples from a climber found in mid-February who is thought to have gone missing in 1972.
Last week, they discovered a second set of what they were describing as historical remains in a different part of the glacier which runs alongside Mount Cook.
Mountain Safety Council spokesperson Andrew Hobman said there was a good chance the body found at the foot of the Tasman Glacier was that of a climber who went missing in 1972.
He said judging by the climbing gear on one of the bodies, they have got a good idea who it might be.
"From our records a pilot witnessed some avalanche debris and some footprints heading towards that debris, two climbers were overdue, they went in and searched and found one but never found the other person and it looks like potentially that is that other person."
Canterbury Police Rural Area Commander Inspector David Gaskin said the two discoveries were from separate incidents and were unrelated.
"The first set of human remains were located on the lower part of the Tasman Glacier with second set recovered from the bottom of the Hochstetter ice fall as it enters the Tasman Glacier," he said.
Mr Gaskin said about 70 people have been reported missing in Aoraki Mount Cook National Park since records began.
He said low snow fall over the winter coupled with warmer temperatures could explain why remains were being found more often this year.
Mr Gaskin said police were working with families who had loved ones missing on the mountain to identify the bodies and hoped they were able to bring closure for some of them.