The joint socket (1) has a concave spherical surface (A) with centre (Ms), while the head (2) has a convex spherical surface (B) with centre (Mk), and is symmetrical in relation to a clamping axis (D) extending in the direction of a neck in the stem (27) of the artificial hip-joint. The surfaces (A,B) have mean radii (R,r), the difference between which is 35 microns. The manufacturing tolerance for surface (A) over an angle between 90 and 180 degrees is less than plus or minus 7.5 microns, while that for surface (B) over more than 140 degrees is less than plus or minus 2 microns. Outside this surface the head is stepped to form a surface (C) of smaller radius from the centre (Mk). Roughness of the surfaces (A,B) is less than 0.08 microns.