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When a normally well behaved cat begins pooping or peeing outside the box, the first thing to check is for a medical reason. If your cat experiences any discomfort while using the box, they will avoid using it, so it might be a good idea to start with having them checked by a vet.
Now, for a little psychology, cats in the wild leave their feces uncovered as a warning to other cats that they have been there and it is their territory. Other cats in turn will respect the other's space and stay away. If you do not have at least one litterbox per cat and they are not cleaned daily, this type of behavior can result. The rule of thumb is one box per cat and one extra, as some cats do not like to share, and some even won't poop where they pee. Moving one upstairs is a good idea, especially if you can put it in the room where this is happening. Another idea would be to place a feedign station over the spot.
Next, if your cat is stressed in any way, change in the household routine, even another cat outside, this behavior can occur. To remedy this, use a Feliway Diffuser in the room they mess in. It emits a calming pheromone scent that the cat finds calming making them feel less like they need to protect their territory.
Lastly, be sure to clean the area with a good enzymatic cleaner to remove all traces of the smell. If they can smell it they will return to it to re-claim. You can also try putting a tarp (not pretty I know) over the area help break the habit. They do not like the feel or sound of them.
Please keep me posted on their progress. We can get them through this.....feel free to contact me anytime for futher help on this is the above does not help. The above steps should cover all possibilites from a medical condition, to territorial behavior and stress, so all bases are covered here.