Logout from portal does not kill session

Hi, 

on a portal (v 8.1) we have implemented the single sign on via a STS server. When I click on "logoff" link I am correctly disconnected. But if I try to login again I am not asked for credentials and the login is done outomaticallly.

This does not happen if I close the browser. 

Is there a way to kill the session when I click on "logoff" and to prevent automatic login even if I don't close the browser?

Thanks.

Regards.