Amelie Mauresmo is a popular player, so there was certainly no widespread rejoicing at her fourth-round defeat at the Australian Open. If there was a voice cheering in the locker room as Lucie Safarova hustled the defending champion out of the tournament, it probably came from Serena Williams.

Within hours of Safarova's 6-4, 6-3 win over the World No.3, Williams reached the quarter-finals at the expense of Jelena Jankovic.

Jankovic was the player in form coming into the event after winning the title in Auckland in the first week of the season and reaching the final in Sydney, but she saved her best performance for the dress rehearsals only to fluff her lines when it came to opening night.

Williams may not be in the best shape of her career, and may have played barely a handful of tournaments over the last two seasons, but she does at least know how to turn up the wattage on her talent when there is a grand slam title up for grabs.

While Jankovic looked tired and bereft of ideas, Williams looked, well, like Williams. She still hits the ball with an almighty thump and though the movement is shorn of much of its grace by her lack of conditioning, her sheer determination to reach the ball allows her to defy the laws of physics.

Jankovic had succeeded in recent matches by hitting her opponents off the court, but no-one has ever been able to do that to Williams. Once the American worked out, mid-way through the first set, that Jankovic had not bothered to pack a Plan B in her racket bag, the Serbian's impressive surge of form in Australasia was destined to come to an end.

Things seem to be falling into place for Williams, who won the title in Melbourne in 2003 - when she completed the famous Serena Slam' by picking up her fourth consecutive grand slam title - and in 2005.

Instead of facing former US Open champion and third seed Svetlana Kuznetsova, as she might have expected to, Williams will play young Israeli Shahar Peer in the quarter-finals.

Peer is an interesting young talent and an impressive and articulate young woman, but she will need to have iron-clad self-belief to beat Williams now that the seven-time grand slam champion has another major title within reach. Williams may only be ranked 81 in the world, but she is not playing like it and her unshakeable, permanently iron-clad self-belief ensures that she probably sees herself as the favourite for the title, let alone the match against Peer.

With Kim Clijsters, Martina Hingis and Maria Sharapova all safely on the other side of the draw, Williams has every chance of making the final, especially now that Mauresmo has gone.

Tenth seed Nicole Vaidisova appears to be the biggest threat but though she was a semi-finalist at Roland Garros last year, she may lack the requisite experience to make the most of her position as the highest ranked player left in the bottom half of the draw.

Safarova is another promising youngster, but the 19-year-old benefited from a rank awful performance from Mauresmo, who never appeared convinced that she was playing well enough to successfully defend her title.

"I'm just, you know, trying to analyze a little bit, you know, the way I played not only today but also throughout the tournament," said Mauresmo.

"I didn't really feel that I was getting too into the tournament just the way I wish I would."

As it turns out, she was right. The only person whose wishes appear to be coming true at this Australian Open is Williams.