A constant velocity joint includes an outer race (1) having a spherical inner surface (2) with track grooves (3) each extending in an axial direction thereof, an inner race having a spherical outer surface (5) formed with track grooves (6) equal in number to the number of the track grooves (3) in the outer race (1), a plurality of torque transmitting balls (7) sandwiched between the inner race (4) and the outer race (1) and accommodated in part in the track grooves (6) in the inner race (4) and in part in the track grooves (3) in the outer race (1), and a cage (8) for retaining the torque transmitting balls (7) while being guided by and between the spherical inner surface (2) of the outer race (1) and the spherical outer surface (5) of the inner race (4). This constant velocity joint of the structure described above is featured in that at least the track grooves (3) in the outer race (1) and an entry chamfer (11) of the outer race (1) are formed by a plastic working process. A method of making the outer race (1) in the constant velocity joint is also provided.