PURPOSE: To shorten the cutting time of the thread groove of a special worm screw by separating a cutting tool from screw base material every time the continuous cutting action of a specified cycle is terminated, and resuming cutting after adjusting the angle-of-rotation position of the screw base material into the initial position of starting slitting to cut the thread groove.

CONSTITUTION: Circular arc shape grooves connecting, at both ends thereof, a going thread groove A to a return thread groove F in relation to an axis are formed by connecting linear grooves B-E and G-J of different lead, and the quantity of cutting depth is increased every time the continuous cutting of one cycle from the groove A to the groove J is terminated. Every termination of the specified cycle, a cutting tool is once separated from screw base material, and cutting is resumed after readjusting the angle-of-rotation position where the slitting of the screw base material is started.