The invention relates to a method for desulphuration of the digestate and biogas in a digester (1) of urban and/or agricultural and/or industrial effluent, by biochemical and/or thermochemical processes, the digester consisting of an enclosure (2) which is closed at the top, in which anaerobic digestion of a mass of products to be treated making up the digestate (4) takes place, the digester comprising at least one loop (10) for external recirculation of the digestate; an oxidant is injected at least at one point (13, 14) of the loop (10), the injection conditions being as follows: the speed of circulation of the digestate in the loop (10) must be high enough to prevent the deposition of sulphur on the walls of the pipes; the contact time between the injected oxidant and the recirculated digestate recirculated from the injection point (13, 14) of the oxidant until the reinjection point (11b) of the digestate must be long enough for all the oxidant to be dissolved in the liquid phase of the digestate; the amount of oxygen in the oxidant injected into the recirculation loop must be low enough to avoid the presence of oxygen in the biogas, but high enough to eliminate the hydrogen sulphide from the biogas.