Process for the separation of a synthesis gas comprising hydrogen, carbon monoxide and methane, and possibly nitrogen, by cryogenic distillation, in which: i) the synthesis gas (1, 5) is purified and cooled down to a cryogenic temperature, ii) the cooled synthesis gas is separated by a first means (9, 15) in order to produce a liquid depleted in hydrogen, the separation carried out by the first means consists of a stage of scrubbing in a scrubbing column with at least a part of the liquid enriched in methane withdrawn from a column for the separation of carbon monoxide and methane having an overhead condenser, the condenser being cooled by a carbon monoxide cycle, and iii) the liquid depleted in hydrogen is introduced into the upper part of a stripping column which also comprises a lower part, iv) a gas enriched in hydrogen (27, 29) is withdrawn at the top of the stripping column, v) a liquid is withdrawn at the bottom of the stripping column and sent to the separation column, a gas enriched in carbon monoxide and depleted in methane is withdrawn at the top of the separation column, a liquid depleted in carbon monoxide and enriched in methane is withdrawn at the bottom of the separation column and the gas enriched in carbon monoxide is heated by heat exchange with the synthesis gas from stage i) in order to form a product, vi) a gas withdrawn in the upper part of the stripping column is at least partially condensed and returned at least in part to the upper part of the stripping column, characterized in that the gas withdrawn in the upper part of the stripping column is at least partially condensed in a heat exchanger which also serves to cool at least one gas (210, 211) withdrawn from the scrubbing column, the heat exchanger also serving to heat a refrigerant. i) the synthesis gas (1, 5) is purified and cooled down to a cryogenic temperature, ii) the cooled synthesis gas is separated by a first means (9, 15) in order to produce a liquid depleted in hydrogen, the separation carried out by the first means consists of a stage of scrubbing in a scrubbing column with at least a part of the liquid enriched in methane withdrawn from a column for the separation of carbon monoxide and methane having an overhead condenser, the condenser being cooled by a carbon monoxide cycle, and iii) the liquid depleted in hydrogen is introduced into the upper part of a stripping column which also comprises a lower part, iv) a gas enriched in hydrogen (27, 29) is withdrawn at the top of the stripping column, v) a liquid is withdrawn at the bottom of the stripping column and sent to the separation column, a gas enriched in carbon monoxide and depleted in methane is withdrawn at the top of the separation column, a liquid depleted in carbon monoxide and enriched in methane is withdrawn at the bottom of the separation column and the gas enriched in carbon monoxide is heated by heat exchange with the synthesis gas from stage i) in order to form a product, vi) a gas withdrawn in the upper part of the stripping column is at least partially condensed and returned at least in part to the upper part of the stripping column, characterized in that the gas withdrawn in the upper part of the stripping column is at least partially condensed in a heat exchanger which also serves to cool at least one gas (210, 211) withdrawn from the scrubbing column, the heat exchanger also serving to heat a refrigerant.