An air distillation unit comprises an air distillation column (10) suitable for producing a nominal flow of gaseous nitrogen, the top of said column being connected to a liquid nitrogen source (8), and operates by carrying out the following steps: a flow of compressed, cooled and purified air is sent to an exchanger (11) and then to the column, a flow of gaseous nitrogen is withdrawn from the column, the level of liquid at the bottom of the column is controlled; and injection liquid (20), sent from the source to the column, is no longer sent if the required production reduces to at most the nominal production. Application to the separation of air by cryogenic distillation.