Unless you are loading the same manufacturer's code when you renew your annual subscription, you must remove the old antivirus product and restart the computer before installing the new one.
A handy pointer to uninstallation tools for each main manufacturer is at:
Having just completed my annual review of reviews of virus protection software, I have found the following products generally better reviewed than the competition:
F-Secure Internet Security 2010
BitDefender Internet Security 2010
Remember to completely uninstall the current protection software and restart the computer before installing either of the above. Also note that it is better to use the current year's product than simply update your subscription to the data files of an earlier generation of product by the same manufacturer.