A charge of scrap is melted in a furnace (1) with post-combustion of the fumes by injection of an oxygenated gas into the space in the furnace above the charge. During periods of post-combustion, the oxygenated gas is injected in the form of several jets each having a flow rate comprised between about 400 and 1200 Nm.sup.3 /h and an injector (11, 12) outlet speed comprised between about 50 and 150 m/s, preferably between about 500 and 900 Nm.sup.3 /h and between about 70 and 125 m/s. Several groups of injectors (11, 12) are used, having an outlet tangential component relative to the vertical axis (X--X) of the furnace (1), successive groups of injectors being disposed at different levels (N.sub.1, N.sub.2) and oriented in alternate circumferential directions. A portion of these injectors have a circumferential component in a first direction and a downward component at a first angle relative to the horizontal, and the other injectors have a circumferential component in an opposite direction and a downward component at a second angle different from the first angle. The oxygenated gas is oxygen having a purity of at least 90%.