A connector for connecting one end of a windshield wiper arm (32a, 32b, 32c) to a first transverse hinge pin belonging to a structure element of a wiper blade unit, the connector being suitable for being received at least in part against the inside end wall of the end of an arm that belongs to a first category of arm, which end is in the form of a U-shaped hook, the connector comprising: - a first recess into which the first hinge pin can be inserted; - a second recess designed to receive a second transverse pin which belongs to a second category of arm that can be of at least a first size, and which extends transversely from a side edge of the end of the arm, - a cylindrical third recess suitable for receiving the end of a third category of arm, which end consists in a shaped-section member segment that extends substantially longitudinally forwards, said third recess being open in its rear face, said second recess being defined in part by - a bottom first tongue that is elastically deformable and that extends substantially longitudinally, a first longitudinal end of which tongue is fastened to the connector, the bottom tongue being suitable for retracting so as to enable the second pin to be inserted, and for causing the second pin to be locked transversely in the position in which it is mounted in the second recess, - a top tongue that is suitable for being received at least in part in a peripheral groove in the second pin so as to lock the second pin transversely, in association with the bottom tongue, the body of the connector comprising a front segment that defines the first recess, the front outside wall of the front segment being suitable for being received against the inside end wall of the U-shaped hook of the arm, a top rear segment and a bottom rear segment, the front longitudinal end of the bottom tongue is fastened to the front segment, the third recess being defined by the front segment, by the bottom face of the rear top segment, and by the top face of a rear bottom segment, the side edges of the bottom tongue being extended transversely outwards by projections and the projections of the bottom tongue extending transversely while passing through an orifice in the associated side wall so that the free transverse end of each projection comes flush with the outside vertical face of the associated cheek plate. - a first recess into which the first hinge pin can be inserted; - a second recess designed to receive a second transverse pin which belongs to a second category of arm that can be of at least a first size, and which extends transversely from a side edge of the end of the arm, - a cylindrical third recess suitable for receiving the end of a third category of arm, which end consists in a shaped-section member segment that extends substantially longitudinally forwards, said third recess being open in its rear face, said second recess being defined in part by - a bottom first tongue that is elastically deformable and that extends substantially longitudinally, a first longitudinal end of which tongue is fastened to the connector, the bottom tongue being suitable for retracting so as to enable the second pin to be inserted, and for causing the second pin to be locked transversely in the position in which it is mounted in the second recess, - a top tongue that is suitable for being received at least in part in a peripheral groove in the second pin so as to lock the second pin transversely, in association with the bottom tongue,