Logging into admin page as new user takes me in as old user

Hi
This is probably really basic stuff, so apologies, but I have tried searching and cannot find a similar post.
When I first installed WP as a complete newbie a couple of years back I setup the initial administrator username up as ‘administrator’ following whatever instructions I was using at the time.
Although I am comfortable that my password is reasonably secure, more recently I have read that to improve security it is best not to stick with that default so, again following advice from various other posts, I created a new user with a much more secure username (and password). I was then successfully able to assign that user super admin rights.

The problem I have is that I cannot login as the new user from the PC on which I did all this. I know the new username & password work, because I have successfully logged in to my control panel from another PC, but if I log out from the administrator panel on my main PC and try to re-log in using the new username and password it does log me in, but as the original user.

Can anyone tell me how to login as the new user on my main computer, so I can then go in and delete the original ‘Administrator’ user?

I have just recently upgraded to WP 3.3.1 and successfully enabled the multi-site functionality.

Any help would be much appreciated!