Abstract: A process of finishing outer joint parts formed in a non-cutting way and intended for constant velocity joints, said outer joint parts having a longitudinal axis and an inner recess which extends in the direction of the longitudinal axis and which, in the direction of the longitudinal axis, is substantially undercut-free, with the inner recess being provided with tracks which comprise contact zones for the rolling contact of rolling contact members, characterized by the following sequence of process stages: non-cutting forming of the outer joint part, surface-layer-hardening of the inner recess at least along the length of the contact zones, for the purpose of producing a hardened surface layer, at least in the region of the contact zones above an unhardened matrix, calibrating the contact zones in respect of their radial positions and axial linearity by displacing the hardened surface layer in the region of the contact zones within the unhardened matrix.