session_id and cookie settings

Hi, when I destroy my session and reload my index.php. I get the same session_id() that was just destroyed before. I've checked it after session_destroy() with echo session(); The function returned no value anymore. But as I said, when starting a new session the old session_id is reappearing. Only when I set off the cookie option in my browser session_start() gives a new session_id. I get really confused with it, because I thought that the session_id is generated by php (a remote machine in my case) and has nothing to do with the browser, exept I would actively set cookies. How can code it that way, that non-independend from the cookie settings in the browser I always can be sure to have a really new session_id? Thank you, Torsten