Abstract: Hinge for fastening a door (12) to a side wall (11) of a piece of furniture, comprising a first element of the hinge (20) fixed to the side wall (11), a second element of the hinge (40) fixed to the door (12) of the piece of furniture, and an intermediate element (60) hinged to the first element of the hinge (20), for allowing the oscillating connection of the first hinge element (20) to the second hinge element (40) to enable the articulation of the door (12) with respect to the side wall (11) of the piece of furniture, the intermediate element (60) being equipped with an adapter (70) suitable for being inserted in a housing (41), incorporated in the second hinge element (40), by means of a linear sliding “drawer-like” movement, the adapter being blocked by the insertion of a tooth (77) on the adapter (70) into a groove (53) and a matching element (54), situated on a lid (52) attached by means of a hinge (48) along the edge of an anchoring plate (50) incorporated inside the second hinge element (40) allowing