A method is provided for treating laundry in a laundry washing machine (220). The washing machine includes: a rotatable perforated washing drum (248) provided with holes and adapted to receive laundry; a washing tub (228) external to said washing drum (248); a water supply circuit (296) including at least one supply valve (302, 308) to supply fresh water into the washing tub (228); a detergent supplier (300) to supply detergent into the washing tub (228); and a rinse additive supplier (306) to supply at least one rinse additive into the washing tub (248). The method includes at least one washing phase during which the laundry is washed with introduction of water and the detergent into the washing tub (228) and tumbled by rotation of the washing drum (248); at least one successive draining phase for draining liquid from the washing tub and following the draining phase at least one rinsing step in which the laundry is soaked with water; and a final rinsing step in which the laundry is treated by means of the ri
