Method for treating water, containing organic matter characterized in that it comprises a step of adsorption of the organic matter contained in said water, in which this water is put into contact with an amagnetic ion-exchanging resin in an infinitely stirred tank (1); the filtering of the mixture of water and resin within the tank (1) and the discharging of filtered water from this tank, the filtering being implemented through at least one screen (4) provided within the tank (1) enabling the resin to be contained in the infinitely stirred tank; the periodic cleansing of the screen (4) consisting of the separation, from this screen, of the saturated resin that has collected thereon; the drawing off (18) of saturated resin from the tank (1); the regenerating (6) of at least a part of the saturated resin thus drawn off; the recycling (7) of said resin thus regenerated in the tank (1); a step of ballasted coagulation/flocculation (12, 13) and separation (14) comprising the addition of coagulant reagent (12b), flocculent reagent (13b) and microballast (21) to the filtered water coming from the tank (1) leading to the formation of flocs; the separation of the formed flocs from a clarified water (16); and the discharging (16) of the clarified water; and the discharging (17) of the sludges formed by the separated flocs.