Updating rubygems - side effects?

Hello everyone.
I’d like to know if updating rubygems will have any effect on the
already installed gems.
I need to update rubygems (very obsolete version) to at least 1.3.5 but
I want to make sure that all the installed gems will work properly after
the update since the machine is running production applications.

Thanks and have a nice day.

Any ideas?

Thanks for any help.