First of all, cats are generally creatures of habit, and hate change. If the cat was using the litterbox properly prior to this, then I would think on if there were any changes at all that could have spurred this change of habit. Like if the box is less clean, changed location, or even if you have changed your routine in a way that could be stressing the cat out. If it's something like that, fixing it probably won't make the cat go back to the proper habit now that it's in the wrong habit, but it will enable you to get it back to the correct habit.
Secondly, you say you have asked your vet about a possible UTI, which is probably the most common medical related cause for suddenly failing to use the litterbox, but it is not the only one. If you haven't already, consult with your vet about the fact that your cat suddenly started urinating outside the box.
Once you've addressed those things, the only thing left to do is to retrain your cat to use the litterbox.
- Put your cat in a small room, like a bathroom, or you can place it inside a kennel, as long as the kennel is just large enough to contain everything the cat needs: litterbox, food, water, toys, and a bed. The point of this is to make it so it's near impossible for the cat to use anything other than the litterbox to eliminate. Cats usually don't like to eliminate on things they use for other activities. Make sure you keep the litterbox as clean as possible, so that it's maximally appealing to the cat. Also make sure to pay enough attention to your cat while it's in this space. This is not meant as punishment, so try to keep it as happy as possible.
- Keep your cat there for some days, perhaps about a week, or until that time that you've judged the cat has been consistently eliminating in its box for some days. During this time, make sure to thoroughly clean your house using cleaners designed to remove pet odors. You want as little smell as possible, so when the cat is ready, it hopefully won't smell anything, and not be tempted to go outside the box again.
- Once you are satisfied things are going according to plan, let your cat go into an additional area of the house. You only want to increase the size of the area it's allowed in a little, so if it's in a kennel, only let it into the room the kennel is in, for instance, or if it's in a bathroom, only let it into the adjoining bedroom. And only let it into the larger area while supervised. If you see it squatting to eliminate, try to distract the cat by loudly clapping your hands, or maybe throwing a toy at it, whatever makes it stop what it's doing. Then, immediately take it back to its litterbox.
- Keep repeating step 3, gradually letting your cat into larger and larger areas of the house. As you come to trust it more, you can then let your cat go unsupervised.
Congratulations, you have retrained your cat.