A method for oxidizing organic matter contained in an aqueous effluent and an installation for implementing the method. The method comprises the following steps: injecting into a tubular body the aqueous effluent; bringing the aqueous effluent to a pressure P1, corresponding to the critical pressure of the aqueous effluent; bringing the aqueous effluent to a temperature T1; and injecting into the tubular body at n points spaced apart from one another, n fractions of at least an oxidizing composition, so that a portion of the thermal energy produced by the oxidation reaction increases the temperature of the reaction mixture from said temperature T1 to temperature T2>T1 according to an increasing curve, whereby the organic matter is oxidized, the reaction mixture continuously developing from a sub-critical liquid state to the supercritical domain.