Martina Navratilova, an 18-time Grand Slam singles champion, says Serena Williams was wrong in her outburst at the US Open women's finals even though she agreed there is a double standard.

Writing for the New York Times, the 61-year-old Czech-born American said a higher standard needed to be observed when Williams called chair umpire Carlos Ramos a "thief" and was penalised a key game in the second set.

"We cannot measure ourselves by what we think we should also be able to get away with," Navratilova wrote. "In fact, this is the sort of behaviour that no one should be engaging in on the court."

Williams, who was thwarted in her bid for a record-tying 24th Slam singles crown in losing to Japan's Naomi Osaka, said she was punished for saying something where men have said far worse without incurring such a penalty.

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"Serena Williams has part of it right. There is a huge double standard for women when it comes to how bad behaviour is punished — and not just in tennis," Navratilova said.

"But in her protests … she also got part of it wrong. I don't believe it's a good idea to apply a standard of, "If men can get away with it, women should be able to, too.

"Rather, I think the question we have to ask ourselves is this: What is the right way to behave to honour our sport and to respect our opponents?"

Martina Navratilova and Bob Bryan win the mixed doubles final against Kveta Peschke and Martin Damm at the 2006 US Open at the USTA National Tennis Center in Flushing Queens, New York. Photo / Getty
Martina Navratilova and Bob Bryan win the mixed doubles final against Kveta Peschke and Martin Damm at the 2006 US Open at the USTA National Tennis Center in Flushing Queens, New York. Photo / Getty

Williams was issued a warning for coaching, something her coach sitting in the stands, Patrick Mouratoglou, admitted to doing.

Williams was unhappy at the violation call and complained to Ramos she hadn't taken any signals.