PURPOSE: To equip a reamer with such factors to be required as dimensional accuracy, roundness, etc. by giving its minor diameter edge a function to carry out machining with good cutting performance and the major diameter edge, with good finishing performance and by allowing them to work cooperatively.

CONSTITUTION: This reamer is equipped with an edge of major diameter 2a and another one of minor diameter 2b concentrically. The chamfering edge 3 of each of them 2a, 2b is so designed that the distance H from the end face of reamer to the cutting edge corner 4 of the edge 2a is greater than that for the edge 2b, that a step is provided in the axial direction, and that the edge 2b precedes in the axial direction for a distance corresponding to H-h. Thus the roundness of an finished hole is very good. That is to say, the edge 2b enhances the cutting performance while the edge 2a, the finishing performance, and they work in preparing better condition for each other.