By coordinating the amount and course of the crowning of the tool and the diagonal ratio, a twist is created with a simple tool, and superimposed on the natural twist, thus resulting in the twist required for the work piece. Furthermore, an additional portion of the crowning is superimposed on the portion of the crowning of the work piece which is the result of the crowning of the tool during the machining in the diagonal method, thus resulting in the required crowning of the work piece, with the additional portion of the crowning being generated by changing the spacing between tool and work piece during the machining.