Anchor for medical use, intended to be inserted into a bone wall, comprising two pieces (2, 3) intended to be assembled with each other, namely an outer piece, intended to be fixed to the bone, which forms an internal longitudinal cavity through it, and an inner piece, intended to be inserted and retained in the said cavity of the outer part, which forms a transverse conduit passing all the way through it; at least one suture thread being intended to be engaged in said cavity by the proximal side of the outer part, to be engaged through said transverse conduit and to emerge from said outer part, by said proximal side; wherein: - the outer part forms at least one first jamming surface arranged in the longitudinal direction of the outer part, and the inner part forms at least a second jamming surface located on the proximal side relative to the transverse conduit, said second jamming surface being arranged in the longitudinal direction of the inner part; - said at least one suture thread is intended to extend along said first jamming surface and along said second jamming surface; - the inner part is movable relative to the outer part between a distal position not blocking the suture thread, in which said second jamming surface is at a distance from said first jamming surface not performing any jamming of this thread, and a proximal blocking position of the suture thread, in which said second jamming surface is at a distance from said first jamming surface performing jamming of this thread, said outer part forming at least a first engagement surface, separate from that first jamming surface, said inner part forming at least a second engagement surface, separate from said second jamming surface, these respective engagement surfaces (15a, 20a) mutually engaging in said proximal blocking position and immobilizing said inner part relative to said part external in this position, characterized in that: said first and second engagement surfaces (15a, 20a) are inclined relative to the longitudinal axis of the anchor so as to be able, when the inner part is moved in the proximal direction inside the outer part, to enter a mutual jamming state that determines said proximal blocking position, and in that said respective jamming surfaces (16a, 25) are arranged such that, in this proximal blocking position, a space exists between them, the thickness of which is about 10 to 40% of the diameter of a suture thread. - the outer part forms at least one first jamming surface arranged in the longitudinal direction of the outer part, and the inner part forms at least a second jamming surface located on the proximal side relative to the transverse conduit, said second jamming surface being arranged in the longitudinal direction of the inner part; - said at least one suture thread is intended to extend along said first jamming surface and along said second jamming surface; - the inner part is movable relative to the outer part between a distal position not blocking the suture thread, in which said second jamming surface is at a distance from said first jamming surface not performing any jamming of this thread, and a proximal blocking position of the suture thread, in which said second jamming surface is at a distance from said first jamming surface performing jamming of this thread, said first and second engagement surfaces (15a, 20a) are inclined relative to the longitudinal axis of the anchor so as to be able, when the inner part is moved in the proximal direction inside the outer part, to enter a mutual jamming state that determines said proximal blocking position, and in that said respective jamming surfaces (16a, 25) are arranged such that, in this proximal blocking position, a space exists between them, the thickness of which is about 10 to 40% of the diameter of a suture thread.