A machine reamer has a base and a reamer head configured as a one-piece indexable insert that axially projects beyond the front of the base. The indexable insert can be introduced in a front insert seat of the base with an axially projecting, preferably conical shoulder and can be clamped therein by a tension rod that extends through the center-axis of the base. In order to improve the rotational catch effect between the base and the indexable insert, the indexable insert has a central polygonal opening through which the tension rod engages with a complementary polygonal section.