Cookie exists after I tell it to expire - and if I set the value it shows up twice.

I've got a cookie called RememberMe. I've written code to write it out if
somebody checks a 'Remember Me' checkbox on a login screen. When I set the
value Response.Cookies('RememberMe') = me.LoginName.Text and then look at
the actual cookies (I have debug set on so I can see all of the assorted
stuff) the cookie is there twice.

Even if I delete the cookie from the Response object, it still shows up.
I've even deleted all of the cookies on my system and it still shows up.

Any suggestion on what am I doing wrong?

TIA - Jeffrey.