1) Right click on your graphical link (left click if your mouse is set up for
left handed use). A screen like this will pop up:

Click on "Image Properties" or hit Alt+Enter.
2) This window will have popped up:

Click on the "Appearance" tab.
3) You will now see this:

In the "Border Thickness:" field put the number
zero
4) It should now look like this:

Now click the "OK" button. You're done. You'll have to
do this for every graphical link on your site, that you don't want a border around.