Why is my Cat peeing on cardboard boxes?

It's possible, the cat's litter box has not been cleaned out or is smelly. Make sure you fully clean out the litter box and any old kitty litter. Wipe clean the inside of the litter box, then use ARM & Hammer Cat Litter Deodorizer on the bottom of the box, before adding new Tidy Cats Cat Litter.   Clean out the litter box daily or multiple times per day if you can.

If your cat's litter box is old, you should think about replacing it with a new High-Sided Litter Box. A cat is very sensitive to smell, so if the litter box stinks, your cat may not want to use it.

If you only have one litter box, which is up or down stairs (in basement), consider getting a second litter box that is easier for your cat to reach on the main floor.  If your cat is older, it may not want to go up and down stairs regularly to go to the bathroom. 

Funny that I should find this entry as I just caught my ‘well behaved’ 14 year old female pee on a large upright flattened cardboard box that had its flaps on the floor. I place cardboard boxes around the basement like this to keep my stuff from getting marked by my spayed alpha 15 year old female. I have 4 adult fixed cats and 5 litter boxes thought the 3 floors we have and I clean them at least once daily. Today I didn’t go into the basement at all until tonight for something I needed.

My 14 year old was down there with me and she peed on the cardboard instead of in the litter box which was 5 feet away.
She strolled into the laundry room where 1 of 3 litter boxes are placed around the basement.
She looked inside, saw an unburied poop (there were a couple of buried ones as well) turned away and went and positioned herself on the cardboard.
I couldn’t believe what I was seeing.
Is she really gonna do this?

Since I’ve never actually ‘seen’ her pee outside the box before and we always blamed the 15 yr old alpha female when I saw pee in numerous places of our home she wasn’t nervous that I’d yell at her.
To her it was only natural not to want to go in a full litter box.
Who could blame her? It was my fault for not cleaning it out this morning, AND this evening.
Lesson learned. 4 cats? 5 litter boxes? Check them ALL twice a day and maybe I won’t have to clean up pee.