A Czech woman whose companion apparently fell to his death on a remote New Zealand hiking track has been found after being stranded for a month, having fashioned a help sign in the snow using fire ashes.

The woman in her late 30s, told police that she had set out on 26 July on the Routeburn Track in the Southern Alps with a male companion also from her country who was in his early 20s. Through a translator, she explained how they got disoriented and spent one freezing night outside. The next day, facing heavy fog, strong winds and snow, they slipped seven metres down a steep slope.

The man fell even further, became trapped and when she got to him, she could not free him and he died.

She then spent three nights in the open but managed to make her way to a warden's hut 2km away which she broke into on 31 July. She survived on its food stores as the area was impassable due to snow.

Otago Tramping and Mountaineering Club spokesman Ian Sime said it was an unusual chain of events, telling Stuff.co.nz: "I can't really understand it at all. It doesn't make sense to me. Five weeks seems a lot. It's unbelievable."

"The Routeburn is not that dangerous. There are not really dangerous banks you could fall down."

Nobody knew the couple was on the track and it was only after relatives in Europe raised concerns on social media that New Zealand police were alerted through the Czech consulate.

Search and rescue teams are reconstructing the scene and hope to recover the body, weather permitting. Police say the death is not being treated as suspicious.

Inspector Olaf Jensen, Otago Lakes central area commander, told the Otago Daily Times that staying in the hut was the right decision.

"No one had been through the hut, and given the severe weather conditions and her physical capability as a result of the ordeal she was not able to make it out and made the right decision in staying put at the hut until rescued," he said.

The popular 32km hiking track, near the tourism hotspot of Queenstown takes about three days to complete. It was the second death on the Routeburn after Israeli tourist Liat Okin, 35, slipped on a boulder and broke her neck in March 2008, after wandering off the main track.

The Czech woman had mild frostbite and hypothermia.