The invention relates to a device for locking two braids (L1, L2) in the form of tapes, the device being for fastening on a wall (S) of an element, and in particular of an intervertebral spacer. It is constituted by a body having a first face (42) for facing the wall of said element, and a second face (44). The body comprises: an axial slot (60) opening out into both faces of the body; two lateral slots (62, 64), each lateral slot opening out into both faces and having dimensions suitable for allowing one braid to pass freely; and two presser surfaces (54, 56) defined in said first face (42) of the body, each presser surface extending between one end of the body and the nearer lateral slot, a flank of each lateral slot co-operating with the associated presser surface to define a first edge (A1, A2), and the other flank of each lateral slot co-operating with the second face of the body to define a second edge (A′1, A′2).