In a method for cryogenically separating a mixture (1) of hydrogen and carbon monoxide optionally including small amounts of methane, argon, and nitrogen for the production of pure CO by partial condensation in one step, the mixture is cooled in an exchange line (3), partially condensed, and at least a portion of the liquid (11) resulting from the partial condensation is sent to the head of a depletion column (15), at least first and second flows (17, 19, 21) rich in carbon monoxide are derived from the depletion column, the first and second flows are cooled at different temperatures, the first flow is sent to a separating pot (27) after expansion, the gas (31) in the separating pot is reheated in the exchange line and sent to the first stage of a carbon monoxide compressor (33, 35, 37) including at least two stages, the second flow is reheated in the exchange line and is sent to a stage of the compressor downstream from the first stage, and the gas in the separating pot and the second flow are reheated in the exchange line at different pressures.