Do you have a few days in which to do this? Here is the method that will lead to the least amount of potential for an accident.
Buy another litter box (you never know when you might need a spare, and besides, it doesn't have to be as nice as the primary box). Take the "used" litter from the current box, put it in the new box, and put that box where you want the new location to be. The "used" litter doesn't have to be full of, shall we say, matter, it can have been cleaned of all the lumps and clumps, but it will still smell right to your cat.
Anyway, after a day or two with two boxes, cleaning on your usual schedule, switch the two boxes: put the old one where you want it to be eventually, and the backup one in the old spot. Once you know for certain your cat is using the box in the new spot, take the old one away. Maybe leave a bathmat or a towel in the old spot, just in case, for a day or two. But if you can rearrange the room so that the old spot is covered by a dresser or something, that will make it much easier. A few squirts of vinegar or citrus will also help.