A cutting unit for cutting blanks for collars of rigid cigarette packets, wherein a continuous strip of packing material is fed in a given direction through a cutting station equipped with a knife having an incision member and a blade, and with a fixed cutting block having a counterblade; the knife oscillates, about a fixed axis crosswise to the travelling direction of the strip, to and from a work position in which the incision member cooperates with a contact surface of the cutting block to incise a portion of the strip upstream from the counterblade, and the blade is located beyond the counterblade to cut the strip along a cutting line.