In Joomla 1.5, you need to press the logout button within the login component, to log off your session.
This logic doesn’t seem very clear for me. If I want to log-off I don’t want 2 page clicks/refreshes.

To create a logout button or menu link, you just need to invoke the logout URL part:

index.php?option=com_user&task=logout&return=Lw==

Or incase when you have Search Engine Friendly (SEF) URL’s:

/logout.html?return=Lw

Now did you note, the return=Lw== parameter?
This parameter is for bringing you back to the return page, after logging out.
The “Lw==”-value, is a Base64 encoding for “/” which brings you back to the root of the page.

Say that you don’t want to forward to the root, but to the ‘/goodbye/index.html’ page?
You will need the Base64 encoding of this string:

/logout.html?return=L2dvb2RieWUvaW5kZXguaHRtbA==

Well, here’s your help, I found a nice online Base64 converter, which does this job for you.

Check out my website to see it working in a Joomla 1.5 page.