Serena Williams, who lost both her temper and her US Open semi-final against Kim Clijsters on Saturday, was last night fined $10,500 (£6,300) and faced with the possibility of suspension for her profanity-laced tirade against a lineswoman who called a foot fault against her.

Officials judged her conduct to have constituted "unsportsmanlike behaviour" and levied the maximum possible penalty. Williams, whose reward for making the semi-final was $350,000 (£209,954), was also fined an additional $500 (£300) for breaking her racket earlier in the controversial match. Suffice to say, she will not be unduly worried by the prospect of financial hardship.More troubling for her, however, is the possibility of further action.

"The grand slam rule book allows for an investigation to be conducted by the grand slam committee administrator to determine if the behaviour of Ms Williams warrants consideration as a major offence, for which additional penalties can be imposed. This investigation has now begun," the referee Brian Earley said in a statement.

Neither Williams nor Earley were prepared to reveal exactly what was said to the lineswoman but the New York tabloids, which splashed the story across the back pages yesterday morning, were not so reticent. Suffice to say, it was not exactly ladylike: "I swear to God I'll fucking take the ball and shove it down your fucking throat."

Even John McEnroe, who is no stranger to controversy, or indeed bad language, was less than impressed, suggesting yesterday that Williams should be suspended. However, taking such a step against the most high-profile figure in the women's game would require a boldness, not to mention a bravery, that most observers believe is beyond the tennis authorities.

Perhaps the most meaningful rebuke will come from the player's mother, Oracene Price, was driven to say of her daughter in the aftermath of Saturday's events: "She could have kept her cool."

Williams was far from apologetic at the time. Indeed, she continued to abuse the lineswoman after her initial tirade, becoming enraged when it appeared she was being accused of threatening her with physical harm, yelling "I did not threaten to kill you. Are you serious?"

Afterwards, she was unrepentant: "An apology from me? How many people yell at linespeople? I see it happening all the time. I don't know how many times I have seen that happen. I am a professional. I'm not the beggar, like, 'Please, please, please, let me have another chance,' because it was the rules and I play by the rules."

Williams, who had been outplayed for most of the match, was playing her best tennis of the night when the trouble started. Having lost only once in seven meetings against Clijsters, she had started as a clear favourite but after losing the first set 6-4, the American's exasperation was obvious as she threw her racket at the court – a code violation that earned her a warning from the umpire. She lost complete control of her emotions in the 12th game of the second set, when she was serving and Clijsters was leading by six games to five and by 30-15.

The lineswoman called a foot fault on the second serve, a marginal call which television pictures were unable to illuminate. It gave the Belgian two match points. Initially, Williams appeared to accept the call but before she could compose herself and get ready to serve again she turned, walked towards to the lineswoman and let rip. Having being warned earlier, she was then penalised a point, which gave the set and the match to Clijsters.