A second ballot on accepting female members at Muirfield will be held, with a decision expected before the end of the year.
The Honourable Company of Edinburgh Golfers (HCEG) - the oldest golf club in the world - voted not to accept women as members in May.
The decision was met with an angry response by politicians, professional golfers and celebrities.
That has prompted a re-think, and a club statement confirmed a "fresh ballot of the membership" would be held.
The statement reads: "The Club Committee has resolved to hold a fresh ballot of the membership and is seeking a clear and decisive vote in favour of admitting women as members.
"A substantial majority of members voted for this change in an earlier ballot but the two-thirds majority required for changes to club rules was not achieved.
"Many members have voiced their disappointment with the result and with subsequent events.
"We expect a second ballot process to complete before the end of the year."
The original vote fell short of the two-thirds majority by just 14 votes, while Henry Fairweather, HCEG club captain, said the committee had recommended the alteration to the rules for approval.
The R&A, organisers of The Open Championship, confirmed Muirfield would no longer be considered as a host venue.
However, they said they would consider the county venue, which last hosted The Open in 2013, if the club changed its policy over female members.
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