A base intended to receive a ski binding thereon, said base comprising a slider (1) fixed to the ski, with a row of notches (4) parallel to the axis of the slider, and a fitted plate (5) sliding onto the slider, with a latch (6) engaged, by the action of a spring, in a notch of the slider, in such a way as to immobilize the plate on the slider, as well as a release lever (13). The latch (6) consists of a fitted part separate from the lever, sliding transversally to the plate, and the base also comprises a mobile element, like a shoe (16) which removes play between the plate and the slider, and may be moved to an active or inactive position by action on the release lever.