Ms Fear, 43, fell into the crevasse at the weekend while climbing with her partner, Bishnu Gurung, who was unable to pull her back to the surface.

There were initial hopes Fear would be found alive after another veteran Australian climber, Lincoln Hall, was rescued over the weekend after having also been given up for dead near the summit of Mount Everest.

But after Mr Gurung returned to base camp late on Tuesday and recounted what had happened to Ms Fear, it was decided she was lost for good, according to a statement from the company that employed her as a guide.

“On consultation with experienced mountaineers, it was concluded that there was no hope of Sue surviving such an incident and that refinding the site of the accident was impossible given the wind and snowfall prevailing in the area,” the statement from World Expeditions said.

“Furthermore, among the only people capable of getting to the site within reasonable time, there was a lack of specialised technical capacity necessary to safely orchestrate the recovery of a body from the depths of such a crevasse,” it said. “Sue’s wish was that if she died in the mountains that her body be buried on the mountain."

Fear’s brothers, Grahame and John Fear, issued a statement saying Australia had lost its “first lady” of mountaineering.

“Sue was a pioneer in Australian female climbing,” they said. “She broke many barriers for females in what remains largely a male-dominated world.

You could never tell Sue, ’You can’t do that’. She would just find a way so she could."

Mr Gurung told colleagues that he and Ms Fear had been walking across a snow field at about 7,600 metres on Sunday when she plunged into the
crevasse.

The two were joined by a rope but Gurung was unable to pull his non-responsive partner up despite 90 minutes of trying. He detached himself from the rope to try rigging up a pulley system but the edge of the crevasse collapsed and the rope anchor pulled loose.

“Looking down all he could see was darkness and there was no response from Sue,” the statement said.

Ms Fear, from Sydney, began climbing at 23 and was the first Australian woman to reach the summit of Mount Everest from the north side.
Mr Hall, 50, meanwhile has been recovering in Kathmandu after cheating death at the top of the world’s tallest peak.

The Australian reached the top of Everest last Thursday but began suffering severe altitude sickness on the descent and two Sherpas accompanying him were forced to leave him behind.

His expedition announced that Mr Hall had died on the mountain, but he was found alive the next morning by another team of climbers, sitting half-dressed and without hat or gloves on the edge of a massive drop.

He was brought back to base camp in a marathon rescue operation and has been undergoing treatment for frostbite and other problems in Kathmandu.

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