Muirfield Golf Club wants to hold a fresh ballot over whether to admit women members just six weeks after rejecting the proposal.
The results of a vote in May revealed 64 per cent of respondents were in favour of the resolution and 36 per cent against, but as the required two-thirds majority was not reached there was no change to policy.
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That resulted in Open Championship organisers the R&A removing Muifield from the tournament rota, although it did say it would reconsider that position if the membership rules were altered.
The Honourable Company of Edinburgh Golfers (HCEG), which owns and runs the Muirfield club has called a special general meeting to seek authority from members to hold a new ballot before the end of the year.
"A substantial majority of our members voted for change and many have voiced their disappointment with the ballot result and with subsequent events," said HCEG captain Henry Fairweather.
"The club committee believes that a clear and decisive vote in favour of admitting women as members is required to enable us to begin the task of restoring the reputation of the club that has been damaged by the earlier ballot outcome."
The result of the first vote, which followed a two-year membership review, was roundly criticised by professionals and politicians.
At the time four-time major winner Rory McIlroy said: "It's not right to host the world's biggest tournament at a place that does not allow women to be members.
"Hopefully Muirfield can see some sense and we can get it back on The Open rota."
Prime Minister David Cameron said the tradition was "outdated" while Scotland's First Minister Nicola Sturgeon described the decision as "indefensible".
Royal Troon Golf Club, which hosts next month's Open Championship, is the only other on the rotation which does not admit women.
A special general meeting is being held next week at which a proposal will be made to allow women to join after a consultation among current members found three-quarters were in favour of changing the constitution of the club.