Removing https:// on outgoing links on a secured page.

I have been on the edublogs dashboard and have observed that when on a secure page https:// the outgoing links are http://.

The reason I ask is I have an ssl on my site and when you go through the registration process all is fine, until you hit the goto admin or the visit your site link as they are secured and the subsite just created is not.

Without using the https on my site it works fine but I think people feel all cozy and warm when submitting signup info on a secured site as opposed to a non secured site.

Is there a way to rectify this?