A rotor (1) for a rotary electrical machine, which includes two pole wheels (2) having a series of axial claw poles (20) of a trapezoidal overall shape which extend axially from the extreme radial outer edge of the pole wheel (2a) toward the other pole wheel (2b), such that each pole claw (20a, 20b) of a pole wheel (2a, 2b) is situated in the space which exists between two consecutive claw poles (20a) of the other pole wheel (2b). The rotor (1) includes magnetic assemblies (3) in the interpole space (22). An assembly (3) is composed of at least one magnetic member (31) and at least one magnet (30), received in a groove (21) made in each of the facing edge faces of the two adjacent claw poles (20a, 20b). This has the advantage of increasing the cross-section for the flow of rotor flux towards the stator, and of enabling the same milling cutter as has already been used to make the grooves in the edge faces of the claw poles.