It reiterated that pilgrims require a Haj visa and it can be obtained through recognised official channels
Williams will now play either Victoria Azarenka of Belarus or Russia’s Vera Zvonareva in the last eight after dismissing Stosur in just 65 minutes in a dominant display.
The world number one remains on track for a semi-final against sister Venus and a possible blockbuster final against Belgium’s Justine Henin.
“Sam beat me last time convincingly so I knew I had to do well out there,” Williams said.
The Australian had gone into the fourth round clash on Rod Laver Arena with some expectation of an upset after beating Williams the last time the pair met.
Stosur had also complained that Williams had not given her much credit for that win, saying the American had implied she was a lucky player, with many of her winners coming from miss hits.
But on Monday she came up against a fiercly determined Williams and simply had no answers.
The defending champion served brilliantly, conceding just two points on serve in the first set and three in the second to completely demoralise Stosur.
The world number one was almost as ruthless on return, breaking the big serving Stosur once in the first set and twice in the second to wrap up a comfortable win.
Williams has continued her love affair with Melbourne Park, where she has won four times, in 2003, 2005, 2007 and 2009.
The 28-year-old has now reached the quarter-finals in Melbourne four times in the last five years and showed against Stosur that she must is the hot favourite to win a fifth crown.
If she does win again it will be the first time a woman has successfully defended her title since fellow American Jennifer Capriati in 2002.
It reiterated that pilgrims require a Haj visa and it can be obtained through recognised official channels
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