The hook has a bore intended to receive an end of an elastic cable. A fastener (2) comprises two branches (7) intended to cooperate with the cable at the level of the bore. The cable is inserted in the bore and the fastener is inserted through a wall defining the bore and through the cable. Free ends (10) of the branches are curved towards each other, and the wall has orifices to receive the branches. An independent claim is also included for an elastic cable equipped, at its one end, with a fixation hook.