A process for separating two gaseous streams, including purifying a first gaseous stream in a first acid gas removal absorber, purifying in a first temperature swing adsorption unit, and then separating at a cryogenic temperature in a separation unit to produce a stream of fluid enriched in carbon monoxide and a stream of fluid enriched in hydrogen, sending a second gaseous stream containing at least carbon monoxide, hydrogen and at least one acid gas to a shift reaction unit, the shifted second stream is purified in a second acid gas removal absorber to remove carbon dioxide and the purified second stream is sent as a feed stream to a pressure swing adsorption unit to produce a hydrogen enriched stream, and sending at least part of the stream enriched in hydrogen from the separation unit as a feed stream to the pressure swing adsorption unit to produce the hydrogen-enriched stream.