In a process for the production of an ammonia synthesis gas, a gas mixture containing hydrogen, argon, carbon monoxide, carbon dioxide and methane originates from a reformer in combination with a combustion unit, the mixture being treated to remove the carbon dioxide which it contains before being cooled and separated in a cryogenic separation unit in a thermally insulated chamber, the mixture being separated to provide a liquid which is vaporized and sent as fuel to the combustion unit having been purified of carbon monoxide and/or methane.