Can't stay logged in

I am on a friends computer so abviously I don't want the computer to remember me. But clicking on the little box to take the check mark out that says remember me when I sign in will not allow me to stay signed in. So, I sign in then start looking around but as soon as I do I am logged out. I had to put the check mark back in so now his computer will think it is me when he visits this site even when I am not here. What can I do? Or can you fix it like other sites have fixed this problem. I have to actually click on a log out button on the other sites to log out, all I'm doing here is clicking on any link and I get logged out.