The electric arc furnace is equipped with a supersonic injector comprising a so-called Laval nozzle arranged at a certain distance above the bath. The dimensions of the nozzle are calculated as a function of the desired flow rate of oxygen and the desired velocity of the jet, and the pressure of the oxygen at the intake of the nozzle is such that the static pressure of the jet at the exit of the injector is substantially equal to the pressure of the surrounding atmosphere. Preferably, the injector comprises an annular channel for injection of natural gas, and can be used in burner mode at the start of the melting of scrap iron. The velocity of the oxygen is then subsonic.