Honing method for machining the inner surface of a bore in a workpiece by means of at least one honing operation, in particular for honing cylinder running surfaces in the production of cylinder blocks or cylinder liners for reciprocating piston engines, wherein in a honing operation an expandable honing tool is used, having in an end region of a tool body that is remote from the spindle an expandable, annular cutting group with a number of cutting material elements which are distributed around the circumference of the tool body and the axial length of which is less than the effective outside diameter of the cutting group with the cutting material elements fully retracted, wherein the cutting material elements are configured as honing segments (220-1, 220-2, 220-3) that are wide in the circumferential direction and narrow in the axial direction such that an axial length of the honing segments, measured in the axial direction, is less than the width measured in the circumferential direction, and wherein on the annular cutting group more than 60% of the circumference is covered with cutting means, comprising the following steps: rigid coupling of the honing tool to a working spindle of a machine tool; relative positioning of the honing tool and the bore in such a way that a tool axis of the honing tool is coaxial with a target position of the bore axis of the bore; inserting of the honing tool into the bore with the cutting material elements retracted, until it is in a final insertion position, in which the cutting group is located in an end region of the length to be machined of the bore that is remote from the inlet; turning of the honing tool and simultaneous expanding of the cutting group at or in the region of the final insertion position into a first radial position of the cutting material elements in such a way that a cylindrical widening of the bore that is substantially centered in relation to the target position of the bore axis is created by the material-removing engagement of cutting material elements on the inner side of the bore in the end region of the bore; withdrawing of the honing tool from the bore with simultaneous turning of the honing tool in such a way that, from the cylindrical widening, the bore is successively widened in the direction of the inlet side. rigid coupling of the honing tool to a working spindle of a machine tool; relative positioning of the honing tool and the bore in such a way that a tool axis of the honing tool is coaxial with a target position of the bore axis of the bore; inserting of the honing tool into the bore with the cutting material elements retracted, until it is in a final insertion position, in which the cutting group is located in an end region of the length to be machined of the bore that is remote from the inlet; turning of the honing tool and simultaneous expanding of the cutting group at or in the region of the final insertion position into a first radial position of the cutting material elements in such a way that a cylindrical widening of the bore that is substantially centered in relation to the target position of the bore axis is created by the material-removing engagement of cutting material elements on the inner side of the bore in the end region of the bore; withdrawing of the honing tool from the bore with simultaneous turning of the honing tool in such a way that, from the cylindrical widening, the bore is successively widened in the direction of the inlet side.