The invention relates to a method for making a cylindrical bore into a conical bore using a honing tool, wherein the honing tool comprises honing stones (13), the length thereof being less than 1/2 the length of the bore to be processed, comprising the following steps: applying the honing stones (13) of the honing tool to the bore; honing the bore over its entire length with a maximum stroke (HMax= OP1 - UP); honing the bore with decreasing stroke (H), wherein a lower reversal point (UP) of the honing tool remains essentially unchanged; and ending the honing process as soon as the upper reversal point (OP) has reached a predefined end value (OP2). In another embodiment, the widening of the bore into a conical shape is carried out by controlling the feed force (Z) with which the honing stones (13) are pressed against the bore according to a position of the honing tool in the bore.