A machine for making absorbent sanitary articles such as nappies for babies or incontinence pads for adults, sanitary towels and the like, comprises a programmable electronic controller device comprising a shift register and at least one optical inspection system connected to the programmable electronic controller device; the programmable electronic controller device generates a synchronism signal having a train of consecutive pulses defining a machine step, a trigger signal for activating the optical inspection system in a synchronised fashion with the synchronism signal and a shift register shift command within a machine step, the programmable electronic controller device also generates an identifier which is uniquely associated with the article inspected by the optical inspection system and sends that identifier with the trigger signal to the optical inspection system; the optical inspection system receives the identifier and, when a response time has elapsed, associates reject information with the respective identifier.