Vista Desktop Icons

I run Vista Ultimate 32 bit.
I make a desktop shortcut to a favourite web page.
Rather than displaying the icon for the link it shows what I assume is a
default icon of the “e� with a blank page behind it.
If I then change the Icon to one I want and apply, it changes.
Then as soon as I click on this icon and the web page opens the icon goes
back to the default.
How do I get it to show the correct icon ?
The correct icon is shown if I right click and select properties.