Method for separating air by cryogenic distillation in a separation unit comprising a medium-pressure column and a low-pressure column, thermally connected to each other, the low-pressure column comprising a sump reboiler and an intermediate reboiler and a column of pure oxygen wherein: i) gaseous air purified and then cooled is sent at a first pressure in an exchange line to the medium-pressure column, ii) oxygen-enriched liquid and nitrogen-enriched liquid are sent from the medium-pressure column to the low-pressure column, iii) nitrogen-enriched gas is taken from the low-pressure column, iv) oxygen-enriched liquid containing at most 97% mol. of oxygen is taken from the sump of the low-pressure column, v) a first flow of oxygen-enriched liquid is sent to a vaporiser and the gaseous oxygen thus formed is sent to the exchange line, vi) a second flow of oxygen-enriched liquid is sent to the top of the column of pure oxygen, having a sump reboiler, where it is purified to form a sump liquid containing at least 98% mol. of oxygen, vii) a flow of pressurised air at a second pressure, higher than the first pressure, is sent to the sump reboiler of the column of pure oxygen, viii) nitrogen-enriched gas is taken at the top of the medium-pressure column, it is sent to the intermediate reboiler of the low-pressure column and the condensed gas is sent to the top of the medium-pressure column, and ix) gas rich in nitrogen or air is sent to the sump reboiler of the low-pressure column and the liquid which is condensed therein is sent to the medium-pressure column characterised in that liquid is taken from the sump of the column of pure oxygen as product, and air pressurised at the second pressure is sent to the vaporiser to vaporise the first flow of oxygen-enriched liquid, and the first flow of oxygen-enriched liquid is less rich in oxygen than the second flow of oxygen-enriched liquid. i) gaseous air purified and then cooled is sent at a first pressure in an exchange line to the medium-pressure column, ii) oxygen-enriched liquid and nitrogen-enriched liquid are sent from the medium-pressure column to the low-pressure column, iii) nitrogen-enriched gas is taken from the low-pressure column, iv) oxygen-enriched liquid containing at most 97% mol. of oxygen is taken from the sump of the low-pressure column, v) a first flow of oxygen-enriched liquid is sent to a vaporiser and the gaseous oxygen thus formed is sent to the exchange line, vi) a second flow of oxygen-enriched liquid is sent to the top of the column of pure oxygen, having a sump reboiler, where it is purified to form a sump liquid containing at least 98% mol. of oxygen, vii) a flow of pressurised air at a second pressure, higher than the first pressure, is sent to the sump reboiler of the column of pure oxygen, viii) nitrogen-enriched gas is taken at the top of the medium-pressure column, it is sent to the intermediate reboiler of the low-pressure column and the condensed gas is sent to the top of the medium-pressure column, and ix) gas rich in nitrogen or air is sent to the sump reboiler of the low-pressure column and the liquid which is condensed therein is sent to the medium-pressure column characterised in that liquid is taken from the sump of the column of pure oxygen as product, and air pressurised at the second pressure is sent to the vaporiser to vaporise the first flow of oxygen-enriched liquid, and the first flow of oxygen-enriched liquid is less rich in oxygen than the second flow of oxygen-enriched liquid.