A rewinding machine arranged to wind a web of absorbent substrate into multiple logs including a perforating module, a cutting module, a winding module and a control module, the web of absorbent substrate travelling into the modules according to a machine direction, wherein the perforating module is arranged to provide the web of absorbent substrate with regularly spaced perforation lines substantially transversally orientated relatively to the machine direction, wherein the cutting module is arranged to sever the web of absorbent substrate substantially transversally relatively to the machine direction, wherein the winding module is arranged to wind the web of absorbent substrate so as to produce logs of web of absorbent substrate, and wherein the control module is coupled to the perforating module and to the cutting module and controls the modules operations.