During the production of rust-free stainless steels, the liquid crude steel is moved to a converter for refining immediately after melting. After the melt is decarburised using oxygen, reduction of the slagged chrome takes place. Desulphurisation is carried out, if necessary, before the final temperature and alloy is set,. In order to achieve an optimum of maximum decarburisation and minimal slagging, an argon-oxygen mixture is injected by means of a lance and/or floor-purging. The ration of argon to oxygen alters according to the duration of the refining process.