I had this same problem with my cat for six long months. She pooped on the linoleum next to the litter box, but would pee in the box. I tried everything - fresh litter, new litter brands, Cat Attract litter additive, laying down newspaper on the floor where she was pooping, moving the box to her poop spot... Nothing worked, although I did try some litter she hated, at which point she also peed on the floor for awhile.

I started trying to catch her in the act. When I did, I would put her in the box. She would then run away and poop on the carpet. I tried containing her to the cat box room - no luck.

I have finally solved the problem. I did a full-fledged cleaning. I took the boxes outside, threw out all of the litter, and washed the boxes in the yard with bleach and a dish scrubber. I then added fresh litter, cleaned the floor in the cat box room, and then put some rubber-backed doormat-type rugs on the entire floor surface in the room to try to discourage her from pooping on the floor (since she apparently preferred the linoleum). She has pooped in the box for the past couple days. I think the bleach is what really did it. I thought replacing the litter was enough, but I think the cat box must itself not have been clean enough for her.