The invention relates to a method for hard fine machining of a pre-manufactured flank (11) of a gear wheel by a machine having at least five axes controlled in coordination and one additional tool axis (WA). According to the invention, a rotation-symmetrical tool (20.1) is driven on the machine side such that it is set into a rotation (RA) about the tool axis (WA). In addition, the axes controlled in coordination are actuated such that a straight-lined section of the surface line of the tool (20.1) is guided tangentially along the flank (11) in a generating movement while the tool (20.1) removes material on the pre-manufactured flank (11) by means of the rotation (R1) about the tool axis (WA). The generating movement follows pre-specified movement vectors (E).