If your cat is peeing in the exact same spot outside of the litter box you need to take certain steps to stop this behavior.
If a certain behavior continues long enough it can be very hard to get your cat to stop doing it.
This is why you need to take immediate action.
The first thing you should do is to clean the spot thoroughly.
Use a cat urine odor neutralizer to clean the spot.
Removing the smell of urine is necessary, because that smell actually attracts the cat back to the same spot.
Next you have to block or eliminate access to that area.
This might be as simple as closing a door, or placing some boxes in the way.
Some people will even put a litter box on top of the area, but in most cases that is not a practical solution.
Who wants to have a litter box next to their bed? In severe cases of cats refusing to use the litter box, I would confine the cat to just one room, until the cat can prove that it can and is willing to properly use the litter box.
Also you should try and figure out why your cat started peeing in the exact same spot all the time.
Normally changes in cat behavior are brought on by stress.
Has there been any changes in the house lately like a new baby or construction? If so, there are many more great techniques that you can use to calm your cat.