Try something like this:
change:
<A href="http://www.mydomain.com">
to:
<A href="http://www.mydomain.com" class="imageborder">
Then in you skin1.css,
you need to add that class:
.imageborder:link {COLOR: #000000;}
.imageborder:active {COLOR: #000000;}
.imageborder:hover {COLOR: #000000;}
.imageborder:visited {COLOR: #000000;}
Not tested, I am presuming that the COLOR bit will alter the border. Other than that, the theory is along those lines.