Originally Posted by OzMan

You would think but you can't be sure unless you have cleared cookies and go to their site and see a new one or search your cookie folder for theirs if you don't wanna delete all.

Check all the other crap too if you haven't already like allowing the site in your browser, javascript and firewall settings.

I think most banks will be moving to this two step process soon so it'd be worth your time to figure it out.