The invention relates to a device for locking two tresses (L1, L2) in the form of ribbons, which can be fixed on a partition (S) of an element, i.e. an intervertebral wedge. It consists of a body having a first surface (42), which is opposite the partition of said element, and a second surface (44). The body comprises: an axial slit (60) opening out into the two surfaces of the body, two side slits (62, 64), wherein each side slit opens out into the two surfaces and the dimensions thereof are such that the tress can pass freely; and two pressure surfaces (54, 56) which are defined in the first surface (42) of the body, wherein each pressure surface extends between one end of the body and the nearest side slit, and one edge of each side slit defines a first edge (A1, A2) with the pressure associated therewith, and the other edge of each side slit defines a second edge (A'1, A'2) with the second surface of the body.