Abstract: In the case of a honing method for machining the internal face (214) of a bore (210) in a workpiece (200) with the aid of at least one honing operation, during a honing operation a flaring-capable honing tool (150) that is coupled to a spindle is moved back and forth within the bore for generating a reciprocating movement in the axial direction of the bore, and are simultaneously rotated for generating a rotating movement that superimposes the reciprocating movement. A bore shape having an axial contour profile which is rotationally symmetrical in terms of a bore axis (212) and deviates from the circular cylindrical shape is generated herein. For generating an axially variable material removal in at least one stroke modification phase a stroke length and/or a stroke orientation of the reciprocating movement is modified.