A method for separating air is provided, in which a flow of oxygen-rich liquid is sent to a top of a pure oxygen column, having a pure oxygen reboiler, in which said flow is purified in order to form a vessel liquid containing at least 98 mol % of oxygen and the vessel liquid is drawn off as a product. A supercharged airflow at a second pressure is sent to the pure oxygen reboiler and to a liquid oxygen vaporizer; a nitrogen-rich gas is drawn from the top of the medium-pressure column and sent to an intermediate reboiler of the low-pressure column and the condensed gas is sent to the top of the medium-pressure column; and a nitrogen-rich gas or air is sent to a vessel reboiler of the low-pressure column and the liquid that condenses therein is sent to the medium-pressure column.