A process for treating a gas stream comprising H2S that includes the step of selectively oxidizing the H2S of the gas stream within a catalytic zone containing an oxidation catalyst and in the presence of an inert liquid medium and molecular oxygen to form elemental sulfur and a gas stream depleted of H2S. A liquid stream yielded from the catalytic zone and containing the inert liquid medium and liquid elemental sulfur undergoes a separation into a first liquid phase rich in the inert liquid medium and a second liquid phase rich in elemental sulfur. Either at least a part of the liquid stream or at least a part of the second liquid phase, or both, undergoes a combustion to form a fluid stream that comprises sulfur dioxide.