The present invention provides a support device. The support device includes a strap, the active length of which is variable, the strap supporting the accessory against the bearing element. The device includes a rail extending between two ends along the strap, the rail is secured to the wall, and a sliding element which slides along the rail, the sliding element includes a passage into which the strap is to be inserted. The device includes an adjustment device for adjusting the active length of the strap. The strap can be extended, relative to the adjustment device, between a retracted configuration, in which the active length is at a minimum, and an extended configuration, in which the active length is at a maximum. The adjustment device includes an element for returning the strap to the retracted configuration thereof.