Others will not use a box that has already been soiled or used by another cat. The single most common reason for a cat's refusal to use a litterbox is because the box is dirty. Non-clumping litter should be scooped daily and the litterbox emptied and washed every other day. Clumping litter should also be scooped daily and the litterboxes washed when soiled. Choose a litter that appeals to the cat.
Most cats prefer the texture of the sand-like scooping litters.
Be sure to choose a brand that clumps into a firm ball, making scooping easier and cleaner. Use caution with scented litter. Most cats have an aversion to perfumed scents. When you wash the litterbox, use a mild dishwashing liquid. Do not use harsh chemicals that will leave an odor.