Apache-AuthCookie logout issue

[Visitor]

I'm using Apache-AuthCookie for authentication. When I access a protected document, i get a login screen which does proper authentication. But when I click on logout, I expect it to delete the session cookie it set. So when I login again, I expect it to ask me for username/password but it allows me access to the protected document.
Please let me know if there's anything I'm missing in the logout process. I'd appreciate any help on this matter.