The invention relates to a franking machine comprising an inkjet printing unit with two printing heads (301A, 301B), for printing on flat posted objects which can be inserted or run through the unit, such as letters or postcards. Said machine further comprises a guide piece (317), arranged around the print heads (301A, 301B) and projecting relative to the common jet opening plane thereof. A transport device for the posted objects is connected to said guide piece, with two drive rollers which, together with the guide piece, form a transport path and which are mounted before and after the print head, relative to the transport direction. The printing heads (301A, 301B) form a common jet opening plane and on the jet opening plane are rectangular in form, arranged at a steep angle to the direction of travel of the posted objects and mutually offset from each other.