A method for honing a rotationally symmetric, non-cylindrical bore includes the steps of limiting the stroke of a honing tool between upper and lower reversal points, continoulsy detecting the actual diameter of the bore at all points along its length between the upper and lower reversal points, continuously comparing the actual diameter of the bore to a specified target diameters for at least one of the upper or lower reversal points, continuously limiting the stroke to regions of the bore in which the actual diameter is smaller than the target diameter, continuously limiting the stroke to regions of the bore in which the actual diameter is smaller than the target diameter, and reducing the stroke of the honing tool step-by-step based on the detected actual values of the diameter of the bore, so that it only the regions of the bore that are machined in which the actual diameter of the bore is smaller than the target diameter corresponding to the detected actual values of the diameter.