Could the Augusta National golf club be forced to make IBM chief Virginia Rometty its first-ever female member?

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The last four chief executives of IBM - a longtime corporate sponsor of the Masters - have been members of the exclusive golf club in Augusta. The latest CEO of the computer giant happens to be a woman. Virginia Rometty was appointed this year.

One problem - a woman has never worn a member's green jacket since Augusta National opened in 1933.

"I think they're both in a bind," Martha Burk said recently. Burk, who spearheaded an unsuccessful campaign 10 years ago for the club to admit a female member, told CNN on Friday that she fears Augusta and IBM will work out a "sham solution" to make the issue go away.

"The company has a huge responsibility here not to undermine its first female CEO," Burk said. "If they accept anything less than full member - or resign their sponsorship, which is another option - they're going to undermine their new CEO. And they'll be making a statement that they don't consider her an equal to her predecessors."