That's great that your cat got a clean bill of health from the vet because there are a lot of medical reasons that can cause this behavior.
But there are also a variety of nonmedical reasons your cat may be urinating outside his litter box, including:
Marking - Cats use urine and feces to communicate with other cats. Urine marking is often characterized by small amounts of urine sprayed on vertical surfaces around the home, especially around windows, doors, and other favored places. Both male and female cats can mark their territory, but it is most common in unneutered male cats. Female cats in heat will also mark. Having your cat spayed or neutered will usually decrease or eliminate this problem.
Litter box aversion - For some reason, your cat may not like his litter box. Cats can be picky about the cleanliness and odor of their boxes. For example, many cats don't like the deodorants in cat litter. Some cats prefer "clumping" litters or deeper litter that they can scratch in and bury their feces and urine. And some cats prefer covered litter boxes, while others prefer open boxes.
For best results, clean the box frequently (scoop the solid materials once or twice daily); put the box in a fairly private area (but not too isolated so he can get to it at all times); be sure the box isn't next to something that sporadically makes a lot of noise (cats have been known to be frightened away from using a box placed next to a noisy furnace or an off-balance washing machine); and offer your cat a couple of different litters in two different boxes (research has shown that most cats prefer nonperfumed, fine or clumping, clay litter).
Social issues - If you have more than one cat, make sure one of them isn't "guarding" the litter box from the others. If you are having problems with a cat not using a litter box, it is recommended that you have one more litter box than the number of cats in the household. This will help make sure that there is always an available, unguarded, relatively clean box for every cat at any given time.
Stress - Stress-related reasons are the most difficult to identify and sometimes to treat. Cats may be stressed by a change in routine, the addition of a new family member or a visitor, a new cat or dog, or even a cat outside that your cat views as threatening. Punishing a cat for urinating out of the box is counter-productive because it adds to the stress level. Treating this problem depends on what the original stressor is. Make sure you are still paying attention to your cat, and try to keep his routine as stable as possible. Be sure that you are still keeping the box clean and feeding him at his regular times. If there is a cat outdoors that is bothering your cat, limit his access to windows and screens so they cannot interact.
Remember, cats don't urinate outside of their boxes to spite their owners; it is often more a sign that they think there is something wrong and are stressed as a result. If this is a continuing problem, medication may be necessary. Be sure to talk to your veterinarian for more information.
