Graham Cox, 60, and two other unnamed people died on Aonach Eagach ridge, Glencoe.
Their bodies were discovered on Sunday after they failed to return home the night before.
One of the climbers was reportedly a mountain guide, though this has not been confirmed officially.
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Police are not treating the deaths as suspicious and a report has been sent to the procurator fiscal.
A Health and Safety Executive spokesperson said: “We are aware of this incident and making inquiries alongside Police Scotland.”
A spokesperson for Police Scotland previously told the PA news agency: “We were made aware of concern for a group of three hillwalkers who had not returned from the Aonach Eagach ridge in Glencoe shortly after 9.05pm on Saturday August 5.
“A search was carried out and the bodies of three people were found.”