I'm pretty sure this can only be controlled at the browser or server level, not at the website level. If you have access to your server, I think you can turn off referrals. Don't quote me on that though.
Larry, the reason why one would want to prevent their site from being shown as a referrer is off topic. I'm just looking for a solution. Feel free to post the question in another thread.
As far as a solution goes, I was hoping not to have to do a redirect. I was hoping there'd be a way to implement a solution on the server level, or through a script that modifies the headers being sent or something.