How to prevent the logined user record is existing when I closed browser.

From: ABC (abc.abc.com)
Date: 10/24/05 

Date: Mon, 24 Oct 2005 10:38:28 +0800

I write a web site with security and role management using ASP.NET's
security management system. Once a user logined, then Close browser.
Re-open Browser to enter web site, the last logined user id is existing.
How can prevent this case?

Thanks