PURPOSE: To bring the configuration of a work piece in a regular circle with out of roundness=0, after completion of one rotation and continue rotation of the work piece to superpose regular while securing a condition of cylindricity=0 and thus superprecise turning process may be achieved.

CONSTITUTION: In both centers supporting system, where the center of a work piece is supported by both centers, a swinging turn of the rotary center 0W is completely eliminated by means of bearings of noncontact type such as pneumatic bearing, fluid static pressure bearing and the like. Turning process with out of roundness=0 shall be so carried out as removing a part shown by slant lines 3 through turning a work piece 2 by means of a cutting tool 1. An edge of a cutting tool TA and the rotary center OW of the work piece are set with no relative motion, and a profile 4 of out of roundness=0 is obtained. Superhigh precision of machining process is obtained by increasing the shank and solidity of the edge of said tool TA.