The invention relates to a constant velocity fixed joint whose outer part (1) and inner part (3) for guiding the balls (5) comprise two alternately arranged sets of first outer running grooves (14) and opposed first inner running grooves (17) which start from opposed open ends (10, 11) and extend in meridian planes in an undercut-free way, as well as second outer running grooves (15) and opposed second outer running grooves (18). To facilitate assembly, the cage (4) arranged between the inner part (3) and the outer part (1) comprises a cylindrical portion whose diameter is smaller than the diameter of a circular free passage in the region of the first open end (10) of the outer part (1).