The invention relates to an assembly (1) for connecting a boot to a ski (2), including a binding (3) arranged to be connected to the boot, and a section (4) of the top surface (5) of the ski (2) arranged to be connected to an essentially plate-like adapter (6) between the binding (3) and the section (4), the adapter (6) being arranged to increase the distance between at least a part of the underside (7) of the binding (3) and the top surface (5) of the ski (2). A first locking device (9) is arranged on the underside (7) of the binding (3) for locking the binding (3) to the adapter (6) via a corresponding second locking device (10) on the top side (11) of the adapter (6). Furthermore, a third locking device (13) is arranged on the underside (12) of the adapter (6) for locking the adapter (6) to the section (4) via a corresponding fourth locking device (14). The first locking device (9) on the binding (3) corresponds in addition to the fourth locking device (14) on the section (4) in order to permit direct connection of the binding (3) to the ski (2) without the use of the adapter (6). The invention also relates to an adapter (6) for use in the assembly (1).