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Muirfield is to be excluded from the Open rota after voting against allowing women golfers to join the club.
Women are currently allowed to play on the Scottish course as guests but they are not allowed into the clubhouse and are prohibited from becoming members.
Following a two-year consultation process on the policy regarding female members, a ballot of the club's members failed to reach the two-thirds majority required to change the rule - 64 per cent voted in favour with 36 per cent against.
"The Honourable Company is a members club, and, as such, the members decide the rules of the club, including its membership policy. Women will continue to be welcome at Muirfield on the course and in the clubhouse as guests and visitors, as they have been for many years," Honourable Company of Edinburgh Golfers (HCEG) captain Henry Fairweather said.
Muirfield last staged the Open in 2013, when it was won by Phil Mickelson but the venue will be removed from the rota while it refuses to admit women members.
"We have consistently said that it is a matter for the Honourable Company to conduct a review of its membership policy and that we would await their decision," R&A chief executive Martin Slumbers said.
"The R&A has considered today's decision with respect to the Open Championship. The Open is one of the world's great sporting events and going forward we will not stage the Championship at a venue that does not admit women as members.
"Given the schedule for staging the Open, it would be some years before Muirfield would have been considered to host the Championship again. If the policy at the club should change we would reconsider Muirfield as a venue in future."
Troon, which stages this year's Open, has separate men's and women's clubs but is currently consulting members over whether to alter its policy.