Our cat did that to for a while. She had always used the litter box before so I took her to the vet. Nothing was physically wrong with her. Well, we got to talking about my work schedule and he decided that my job was the problem. I had recently started working 12 hour shifts, 6 days a week and the vet thought that Emma was acting out. I couldn't change my hours so I started skimping on my house work in order to have more time with her. She stopped doing it after about a week. My vet also mentioned that if that didn't work, there was a special kind of kitty litter that had some kind of cat attractant in it. I don't remember what it was called anymore but maybe your vet would know. Good luck!!!