Described is a machine for making absorbent sanitary articles, such as nappies, sanitary pads and the like, where each article (2) comprises a plurality of components (8,9) progressively positioned relative to each other and assembled along a production line (3) through a plurality of operating stations (24,25,26,27,28,29,32,35) equipped with devices for cutting and/or sealing the materials the articles (2) are made up of and at least one rejection station (39) downstream of the operating stations; the machine (1) comprises a programmable electronic controller device (42) having a shift register (40), at least one optical inspection system (36) connected to the programmable electronic controller device (42), and an operator interface (51) connected to the electronic controller (42); the programmable electronic controller device (42) generates a machine (1) sync signal (43), a trigger signal (46) for activating the optical inspection system (36) in phase with the sync signal (43) and a shift register (40) shift command (47); the optical inspection system (36) receives the trigger signal (46) and has a defined maximum response time (T) which produces at least one band of uncertainty (48); the operator sets with the operator interface (51) the instant of activating the shift register (40) shift command (47) outside the band of uncertainty (48) and between two consecutive sync signals (43) defining a machine step (45).