NOVELTY - The process comprises injecting gaseous or liquid oxidant in a point (13, 14) of a recirculation loop (10) of a digester (1), where the recirculation loop is external of digestate (4). The digester is constituted by an enclosure (2) closed at the top. An anaerobic digestion takes place with a mass of products to be treated forming the digestate with a gas volume above the digestate from which the biogas is removed. The injection step is carried out by conditions of: a speed of movement (1 m/s) of the digestate in the loop sufficient to prevent sulfur deposition on conduit walls.    USE - The process is useful for desulfurizing digestate and biogas in a digester of installation of wet and/or dry urban, agricultural and/or industrial effluents for treatment of: wastewater; household waste such as fermentable fraction of household waste and/or domestic waste; agriculture waste such as manure and crop residue; and waste from restaurants, canteens and unsold supermarket.    ADVANTAGE - The process ensures simple, efficient and economical desulfurization of digestate and biogas in the digestate without malfunction and any risk of damage to the digester, and prevents the appearance of stalactites under the dome of the digester.    DETAILED DESCRIPTION - The process comprises injecting gaseous or liquid oxidant in a point (13, 14) of a recirculation loop (10) of a digester (1), where the recirculation loop is external of digestate (4). The digester is constituted by an enclosure (2) closed at the top. An anaerobic digestion takes place with a mass of products to be treated forming the digestate with a gas volume above the digestate from which the biogas is removed. The injection step is carried out by conditions of: a speed of movement (1 m/s) of the digestate in the loop sufficient to prevent sulfur deposition on conduit walls of the recirculation loop; a contact time (15 seconds) between the oxidant injected into recirculated digestate from injection site of the oxidant to the point of reintroduction of digestate in the chamber sufficient for the oxidant dissolved in the liquid phase of the digestate; and a amount of oxygen in the oxidant injected into the digestate sufficiently low to avoid the presence of oxygen in the biogas, but sufficient strong for the removal of hydrogen sulfide from the biogas, where the produced sulfur remains in the form of particles dispersed in the digestate and is evacuated with it. An amount of air or oxygen injected into the recirculation loop corresponds to an equivalent concentration of oxygen of 0.60-0.20 X, where X is the saturation concentration of oxygen in pure water estimated at the temperature and pressure of the recirculation loop. The injected oxidant is gaseous and is constituted by air or oxygen. An INDEPENDENT CLAIM is included for an installation for production of biogas.    DESCRIPTION OF DRAWING(S) - The diagram shows a schematic view of an installation with a digester.    Digester (1)    Enclosure (2)    Digestate (4)    Recirculation loop (10)    Injection point. (13,14)