From what you have told me, it appears that your cat is suffering from some type of stress that has caused this inappropriate elimination. This could be due to a territorial issue or some other stress such as being left alone. The first thing you need to do is to purchase from any pet store a product called Feloway. This is a feline pheromone that acts as a calming agent and will discourage this bad behavior. Follow the directions on the bottle. Next, make sure to change all litter boxes to different places especially where there is little traffic. Keep these boxes extremely clean. If this is not sufficient, your vet has medication that can help with this problem and, if used along with the Feloway, hopefully, will be successful. Here is a website that has more tips:
www.petplace.com/cats/inappropriate-elimination/page1.aspx
Good Luck!!
Cat Veterinarian
25 years experience treating cats in my practice