A reversible cutting insert for milling has first and second cutting edges formed at the transitions from the top and bottom surfaces to a lateral face. The cutting insert has a 4-fold rotational symmetry. A reference plane extends perpendicular to the axis of symmetry. The cutting edges have four cutting edge portions. One cutting edge portion is a main edge and a wiper edge that are connected by a rounded cutting corner. The first and second cutting edges are at the greatest distance from the reference plane in the region of the cutting corners. Main and wiper clearance faces directly adjoin an assigned main edge and wiper edge, respectively, in the circumferential lateral face. Exterior angles between the main clearance faces and the reference plane are greater than exterior angles between the wiper clearance faces and the reference plane.