I was hoping to get some additional information from you, but I didn't want you to go without an answer for so long.
If this is purely a behavioral issue, it can be caused by a variety of factors. First, keep the litterbox on the second floor, if you're not already doing that. Next, add 'Cat Attract' clumping litter to both litterboxes. This litter contains herbal attractants which encourage use of the litterbox. This is sold in pet supplies stores or can be ordered online:
Make sure to place each litterbox in an easily accessible area that is not in the path of the household traffic and not near any noisy appliances. It would be a good idea to add yet a third box (open) and use only unscented litters. Also, make sure to wash all litterboxes at least once a week, with mild soap and warm water, plus a little baking soda; rinse well and dry. If the two boxes you have already, have been in use for a few years, replace them with new ones, because the plastic of the box does absorb odors that will never come out, no matter how well you clean them. Make sure to scoop the boxes a few times a day, so they're almost always clean. Some cats are very fussy.
Get two Feliway plug in diffusers and a Feliway spray. This product contains a cat-calming pheromone and helps in cases of inappropriate elimination. Here is more information:
Cats 'speak' with their waste; it's most likely that your cat is 'marking' territory with her feces. This can be brought on by many causes: stress, anxiety, frustration. For example, if you have recently rearranged the furniture in your livingroom or had any renovations, painting, new carpet, a new appliance, etc., this can make her feel anxious and upset, because cats are creatures of habit. By 'marking' in certain areas, she's declaring 'THIS IS MINE!' and it makes her feel no changes can take away HER place or her usual places in the house. Even if you change the angle of a chair in a room she frequents or sleeps on, this is enough to make her feel stressed/anxious.
It's essential that you clean the areas she soils with an enzyme-based cleaner for organic/pet stains and odors. Some well recommended ones are: Nature's Miracle, Zero Odor, Odor Mute, and many more available in your pet supplies stores, home improvement stores, and places like Walmart, Target, etc. The purpose of this, is the enzyme action completely removes the scent of where she went in the past and if she no longer smells it, she doesn't think it's an appropriate toileting area.
After cleaning these areas thoroughly, allow to dry and then spray lightly with Feliway. This will make her feel she's 'marked' there already and she will not return.
Another stressor that might be possible and a very common one, is if she likes to look out the windows and sees/smells another cat (stray or neighbor cat) coming around your house. This is threatening to her and causes her to start marking to assert her dominance and as I mentioned above, to declare this is MY territory--do not trespass. It would be advisable to spray the window sills and window frames with Feliway and also spray around any doors leading to the outside. You have no idea if a stray cat is 'marking' territory around YOUR house. You might smell cat urine outside, but then again, you might not. Spray the outside frame and bottom of the outside doors, as well, to mask the scent of any strays. Don't allow her access to the sprayed areas inside, until they're completely dry--about 30 minutes.
Try to enrich her environment with a tall cat tree or kitty condo, if you don't yet have one, and some new toys, in case she's bored and feels she's not getting enough attention. Here is a great list of toys she can play with herself and interactive toys:
As frustrating as it is, don't yell at her after the fact, because she will not know what you're talking about. If you catch her in the act, say firmly, 'no!' then pick her up and place her in the nearest litterbox. Put the stool in the box as well, to remind her that's where it belongs. Don't yell and scream or she will come to be afraid of YOU. You want her to know her 'action' is the wrong thing to do, and associate YOUR action with what she's doing at the time.
You didn't mention if the vet did a fecal analysis or not, and I'm glad his physical exam proved she's healthy, but if a fecal wasn't done, please bring him a fresh sample to test for intestinal parasites. This is a very common reason for cats to eliminate outside the box. Sometimes, it takes a few fecal tests to determine if any eggs, larvae or parasites are present, because the one section tested may be negative, even when intestinal parasites are present.
I hope things improve, soon!
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