For any anchor tags within the iframe, try setting the target to _self. Like this:
<a href="/mynewlinkwithiniframe.html" target="_self">Test</a>
I'll play around with it, but I know this was the standard for old school frames.
EDIT Based on some tests I did, the default action for anchor links within an iframe is to load the new content within the iframe. target="_self" is redundant unless there is something else overriding it. Maybe you should supply more info about the source code if this isn't resolving it for you.
I could also make an assumption that you are running into the problem using javascript. If you are using window.location.href, you'll want to change that as follows:
Instead Of:
window.location.href = 'newpage.html';
Try:
window.open('/newpage.html', '_self');