Advice on Removing a Litterbox

Hello,

Currently, we have 2 cats and 4 litter boxes. Each cat sleeps in a different room, and each of those rooms has a litter box. In the living room and common area, there are 2 litter boxes, only 6 feet apart. We are planning to get an automatic litter box and replace one of the living room boxes with it. After we introduce them to it and (hopefully) get them used to it, we would like to remove the uncovered litter box. Any advice to cause the least amount of accidents?