A side air bag for a vehicle occupant restraint system of a motor vehicle is provided. The side air bag comprising at least one inflatable chamber, having a first area to protect the head of a vehicle occupant as well as a second area which—referring to the state of the side air bag (in which it is installed in the vehicle and inflated—extends in the direction of the vehicle floor beyond a door parapet which is adjacent to a side window of the vehicle. The chamber is designed in such a way that it tapers off from the first towards the second area.