Carbon monoxide is generated carbon monoxide, in a conversion stage (DR), from a hydrocarbon-containing feed (1, 2), and also steam and/or carbon dioxide (CO2), resulting in the formation of a carbon monoxide (CO)—, hydrogen (H2)— and methane (CH4)-containing synthesis gas (3). The synthesis gas is subsequently fed to a fractionation device (Z) for separating off at least one hydrogen-rich fraction (7, 9) and one methane-rich fraction (10) and also a carbon monoxide product (6). The methane-rich fraction (10) separated off in the fractionation device (Z) is recirculated as feed (M feed) upstream of the conversion stage (DR).