Device for installing a headrest on a backrest of an automobile seat

The device (1) has an assembly support (7) arranged to allow a transverse angular displacement of a sheath (4), around a lower end of the support between a latching position and a sliding motion position. A projection (5) fits in a notch in the latching position, and projection is removed from the notch in the sliding motion position so as to allow a sliding motion of a rod in the sheath. A spring (8) actuates the sheath toward its latching position, where placement of the sheath in the sliding motion position is done by pressure of a user on a support zone in opposition of the spring. The spring is in form of an elastic blade interdependent of the sheath. The support is in form of casing.