A method for separating air by cryogenic distillation in a system of columns comprising a first column and a second column operating at a lower pressure than the first column, comprising the steps of compressing all of the feed air in a first compressor to a first output pressure of at least 1 bar greater than the pressure of the first column, sending a first portion of the air under the first output pressure to the second compressor, and compressing the air to a second output pressure, cooling and condensing at least a portion of the air under the second output pressure in a heat exchanger, withdrawal of a liquid from a column of the system of columns, pressurising the liquid and evaporating the liquid by heat exchange in the heat exchanger, and pressure reduction of a portion of the compressed air to a second output pressure, at least partially evaporating said air in the heat exchanger, optionally additional heating of said air in the heat exchanger, and sending at least a portion of this air to the second compressor.