The invention relates to a headrest having two rods (2), at least one having a locking detents, a housing with two channels and two sets of bearings, each set comprising a top bearing and a bottom bearing. Each bearing set is mounted in a corresponding channel by fitting these bearings into receptacles. The bearings have openings in which the rod can slide and a locking device for locking the housing relative to the rods in a plurality of vertical positions. The device includes at least one locking projection movable relative to the housing between a locking position and an unlocking position. The two rods are part of a frame formed by a metal tube bent to take the general shape of an inverted U with the rods corresponding to the legs of the U.