It could be a number of things.
1: Cat pee contains ammonia, and no matter how much you clean an area where she pees, the scent will never really go. This is why your cat keeps peeing on the floor - she is being attracted to the smell. Have you noticed if she pees in exactly the same places every time? Has she ever used her litter box? Speak to your vet about reccommending suitable cleaning products (this could be done over the phone)
2: She could have a problem that means she can't control her pee. This could be quite dangerous and you should see a vet.
3: She may be really fussy about the type and quantity of cat litter you use (cats are very fussy!)
Our cat used to do the same thing (but always only half a metre outside the litter tray). Every couple of hours we would place Ollie in the litter tray, just in case he needed to go. Also, whenever he did use the litter tray, we would congratulate him and reward him.
A word of warning - don't punish your cat, as cats don't really understand. They tend to associate YOU with the punishment, not the bad behaviour.