The victim, who was one of four Danish climbers on the expedition, was on his way down from the Rimpfischhorn mountain in Valais in the south of the
country when he fell.
The party was not roped together when the 44-year-old fell at an altitude of 4,100 metres (13,451 feet), police said in a statement.
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A mountain guide raised the alarm and a doctor attended the climber who was pronounced dead at the scene, police said.