An end joining piece (4) for a windscreen wiper for a glazed surface of a motor vehicle is disclosed. The end piece has at least a receipt receptacle (410) for receiving an end part of a longitudinal vertebra (20), and at least one flexible tongue (6a, 6b) which is configured to go from a first, position of rest, to a second, retracted position, by displacement in a first direction (F2a, F2b) during the insertion of the longitudinal vertebra in the receipt receptacle (410), the flexible tongue including an engagement ramp along which the vertebra is made to thrust, to provide the tongue with its second, retracted position. The engagement ramp (620a, 620b) has an inclination which is configured to exert on the longitudinal vertebra a force which tends to displace this vertebra in a second direction (F3a, F3b), which, together with the first direction of displacement, forms a non-zero angle.