Method of making a thread on a cylindrical, conical or frustoconical workpiece, comprising the steps of: a) driving in rotation the workpiece in one direction, b) carrying out a relative displacement of a first cutting edge of a tool (5, 11, 20, 29, 32) relative to the workpiece until this first cutting edge is flush with the surface to be threaded of the workpiece at the beginning of the section to be threaded, c) carrying out a relative displacement of the tool (5, 11, 20, 29, 32) relative to the workpiece so that the first cutting edge machines the workpiece, d) carrying out a relative displacement of the tool (5, 11, 20, 29, 32) along the longitudinal axis of the workpiece, in one direction until the end of the section to be threaded, e) moving away, by a relative displacement, the first cutting edge of the tool (5, 11, 20, 29, 32) from the workpiece, wherein it further comprises the steps of: f) reversing the rotation of the workpiece to drive this piece in rotation in the direction opposite to the direction, while positioning or not the second cutting edge, g) moving, by relative displacement, a second cutting edge towards the workpiece until this second cutting edge penetrates the thread pitch, h) carrying out a relative displacement of the second cutting edge relative to the workpiece so that it continues the machining of the thread in this piece, i) carrying out a relative displacement of the second cutting edge in a direction opposite to the direction, until the beginning of the section to be threaded, j) moving, by a relative displacement, the second cutting edge away from the workpiece, k) reversing the rotation of the workpiece, while positioning or not the first cutting edge, and l) repeating steps b) to k), while continuing the machining of the thread, until the thread reaches its final dimensions, while positioning the first cutting edge in step b) in such a way that it penetrates the thread pitch already machined. a) driving in rotation the workpiece in one direction, b) carrying out a relative displacement of a first cutting edge of a tool (5, 11, 20, 29, 32) relative to the workpiece until this first cutting edge is flush with the surface to be threaded of the workpiece at the beginning of the section to be threaded, c) carrying out a relative displacement of the tool (5, 11, 20, 29, 32) relative to the workpiece so that the first cutting edge machines the workpiece, d) carrying out a relative displacement of the tool (5, 11, 20, 29, 32) along the longitudinal axis of the workpiece, in one direction until the end of the section to be threaded, e) moving away, by a relative displacement, the first cutting edge of the tool (5, 11, 20, 29, 32) from the workpiece, f) reversing the rotation of the workpiece to drive this piece in rotation in the direction opposite to the direction, while positioning or not the second cutting edge, g) moving, by relative displacement, a second cutting edge towards the workpiece until this second cutting edge penetrates the thread pitch, h) carrying out a relative displacement of the second cutting edge relative to the workpiece so that it continues the machining of the thread in this piece, i) carrying out a relative displacement of the second cutting edge in a direction opposite to the direction, until the beginning of the section to be threaded, j) moving, by a relative displacement, the second cutting edge away from the workpiece, k) reversing the rotation of the workpiece, while positioning or not the first cutting edge, and l) repeating steps b) to k), while continuing the machining of the thread, until the thread reaches its final dimensions, while positioning the first cutting edge in step b) in such a way that it penetrates the thread pitch already machined.