A method of producing a carbon dioxide product stream from a synthesis gas stream formed within a hydrogen plant having a synthesis gas reactor, a water-gas shift reactor, located downstream of the synthesis gas reactor to form the synthesis gas stream and a hydrogen pressure swing adsorption unit to produce a hydrogen product recovered from the synthesis gas stream. In accordance with the method the carbon dioxide from the synthesis gas stream by separating the carbon dioxide from the synthesis gas stream in a vacuum pressure swing adsorption system, thereby to produce a hydrogen-rich synthesis gas stream and a crude carbon dioxide stream and then purifying the crude carbon dioxide stream by a sub-ambient temperature distillation process thereby to produce the carbon dioxide product. A hydrogen synthesis gas feed stream to the hydrogen pressure swing adsorption unit is formed at least in part from the hydrogen rich stream.