Cannot uninstall and then reinstall Adobe Air

It has been working fine before; the BBC iplayer ask me to reinstall Adobe Air recently.

I have manged to uninstall AA from the program list (but not sure if it is done correctly). When I try to reinstall AA, a message state that 'Adobe Air is already installed on your computer'.

How can I make sure that AA is actually uninstall from my computer.

Thanks,

Gordon