In a zero-clearance radial ball bearing, two outer bearing race sections (4, 5) made by non-cutting methods together support an outer race (2) while between it and a concentric inner race (3) run bearing balls (1). Against the first bearing race section (4) bears a sleeve section (7) which circumferentially and axially surrounds the second race section (5). A spring component (10) pressing the two race section (4, 5) together acts between the sleeve section (7) and the second bearing race sections (5) in such a way that the balls (1) run with zero clearance. In order to improve the rigidity of such a radial ball bearing and especially the sleeve section (7), it is proposed that the two axial ends of the sleeve section (7) project axially beyond the balls (1). The sleeve section (7) is folded at its end away from its free end to form a radially internal cylindrical stiffening section (13) arranged concentrically with the sleeve section (7) which extends as far as the center of the balls (1) and on which bears the first bearing race section (4).