Abstract: In accordance with the invention, the workpiece (1) is mounted on a lathe headstock spindle rotated by drive means about a headstock spindle axis (I--I). A turning tool (3) is mounted on a toolholder carriage adapted to move in translation along an infeed axis (III) and along a carriage axis (IV). The turning tool (3) has a cutting edge (4) made up of a plurality of cutting edge portions adapted to be individually engaged with the workpiece (1). The turning tool (3) is rotated about an axis (II) which is not parallel to the headstock spindle axis (I--I) to bring the separate portions of the cutting edge (4) of the turning tool (3) successively into contact with the workpiece (1). The invention can be used to cut helical threads.