In an air-distillation method, purified air is cooled in an exchange line (8) and then sent to a distillation column (12) of a system of columns, and oxygen- and nitrogen-rich fluids are extracted from a column (14) of the system of columns only during the repressurization phase. A purified airflow, constituting between 3% and 20% of the air compressed in the compressor, is used to at least partially pressurize the adsorber completing the regeneration phase thereof, and the airflow compressed in the compressor during the adsorption phase is substantially equal to the airflow compressed in the compressor during the pressurization of the adsorber. A portion of the purified air is sent to a turbine (27) where it is decompressed and then sent into the atmosphere so as to ensure that it is kept at least partially cold during the entire cycle, and the amount of decompressed airflow sent into the air during the pressurization of an adsorber is less than the amount sent into the air during the adsorption phase of the same adsorber.