There is described a printing machine for printing sheets, in particular sheets for the production of securities, banknotes, passports, ID cards and other valuable documents, comprising at least a sheet feeder, a printing unit, a delivery unit with delivery piles for the printed sheets and a sheet transport system for transporting the printed sheets along a transporting path from the printing unit to the delivery piles. The printing machine further comprises a laser perforating unit with at least one laser head disposed along the transporting path of the sheet transport system for perforating the printed sheets, and a first aspiration unit to maintain the printed sheets against an aspiration surface during perforation by said laser perforating unit.