Honing method for machining the internal face of a bore in a workpiece with the aid of at least one honing operation, in particular for honing cylinder running faces in the production of cylinder blocks or cylinder liners for reciprocating piston engines, wherein during a honing operation a flaring-capable honing tool 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 is 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 and deviates from the circular cylindrical shape, is generated, and 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, a honing tool which has an annular cutting group having a plurality of radially actuatable cutting material members that are distributed about the circumference of a tool body is used, during the stroke modification phase a measurement of the actual diameter of the bore is carried out for determining a diameter measurement signal which represents the actual diameter of the bore in a measurement plane, and the stroke length and/or the stroke orientation of the reciprocating movement is controlled as a function of the diameter measurement signal, characterized in that for determining the diameter measurement signal a measured value detection takes place by way of a floating mean value, wherein the floating mean value is determined in a portion of the bore or across the entire currently machined portion of the bore. during a honing operation a flaring-capable honing tool 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 is 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 and deviates from the circular cylindrical shape, is generated, and 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, a honing tool which has an annular cutting group having a plurality of radially actuatable cutting material members that are distributed about the circumference of a tool body is used, during the stroke modification phase a measurement of the actual diameter of the bore is carried out for determining a diameter measurement signal which represents the actual diameter of the bore in a measurement plane, and the stroke length and/or the stroke orientation of the reciprocating movement is controlled as a function of the diameter measurement signal, characterized in that for determining the diameter measurement signal a measured value detection takes place by way of a floating mean value, wherein the floating mean value is determined in a portion of the bore or across the entire currently machined portion of the bore.