The invention relates to a method for separating air by cryogenic distillation in a separation unit including a medium-pressure column (23) and a low-pressure column (25), in which a flow of oxygen-rich liquid is sent to the top of the column of pure oxygen, having a vessel reboiler (61), 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 higher than the first pressure is sent to the vessel reboiler of the pure oxygen column and to a liquid oxygen vaporiser (51); a nitrogen-rich gas is drawn from the top of the medium-pressure column; said gas is 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 (36) of the low-pressure column and the liquid that condenses therein is sent to the medium-pressure column.