For a trailer coupling, the fixing unit has a stationary first toothed segment which is fixedly connected to the pivot bearing base. A first toothed segment which in the working position is connected to the pivot element in a rotationally fixed manner and pivots together with same and is engageable by displacing the pivot element from the pivot position into the fixed position, and is disengageable by displacing the pivot element from the fixed position into the pivot position.