An attachment to a milling machine having a rotary drive, particularly useful for cutting sharp interior corners in a workpiece, comprising a rotary shaft couplable to the rotary drive of the milling machine so as to be rotatable about the shaft's longitudinal axis. The attachment further comprises a conical cutter member having a rotary axis, an apex located on the axis, and at least one external conical surface portion having a leading end at the apex and a trailing end spaced apart from the rotary axis and from the apex along the rotary axis. The conical cutter member has a cutting edge constituting a part of the conical surface portion and extending between the leading and trailing ends thereof. The rotary axis of the conical cutter member is oriented transversely though not perpendicularly to the shaft longitudinal axis. The conical cutter member being coupled to the rotary shaft so as to be rotated about the rotary axis by the shaft, upon the shaft's rotation about the longitudinal axis.