Abstract: The invention relates to a high-precision revolving center (10) for machine tools. Prestressed bearings 40 and 45 are brought into abutment on the one hand against internal 33 and external 25 cylindrical surfaces whose deviation, at any point on the surface, with respect to the theoretical surfaces centered on the axis, is less than 1 .mu.m, and on the other hand against reference surfaces 26 and 34 perpendicular to the axis. Threaded elements 50, 55 enable the bearings 40, 45 to be stressed. Once the center 10 has been assembled and the bearings stressed, the revolving center is mounted on a grinder in order to give a precision finish to the tip 90, the concentricity reference surface 91 and the perpendicularity reference surface 92.