A double-sided cutting insert for milling, in particular for face milling, includes first and second cutting edges each having alternately disposed main lips and secondary lips which each extend between active and passive cutting corners. Each main lip, starting from a first distance from a reference plane at an active cutting corner, extends in a manner dropping monotonously to a smaller, second distance from the reference plane at a passive cutting corner. That end of a secondary lip that adjoins the active cutting corner is in each case at a greater distance from the reference plane than the other end of the secondary lip that is remote from the active cutting corner. A circumferential side surface has, immediately adjacent the secondary lips, in each case planar secondary flanks and each secondary lip is formed at least regionally in a convex manner in plan view of the associated secondary flank.