Ah, you'll need to follow the 6.0.2 to 6.1 instructions. Basically 6.0.2 and 6.0.3 are the same except for a couple security changes so the instructions apply to both.
Normally you should get a message stating "Done" when the upgrade is complete. If not, you might be able to just open another browser window and go to your forums after a minute or two.
-------------------
Rick Baker
UBBThreads developer