The invention concerns glass-metal sealing comprising effecting on a metallic piece, in particular an alloy based on iron and nickel or iron, nickel and cobalt, first of all a decarburization under an atmosphere, at a temperature of between 950.degree. C. and 1,150.degree. C., formed by hydrogen (10 to 99%), water vapor (1 to 8%), with a ratio hydrogen/water vapor higher than five, the possible remainder being nitrogen, then an oxidation under an atmosphere formed by an inert vector gas such as nitrogen, either at a temperature of 600.degree. C. to 800.degree. C. and with a water vapor content of 8% to 2%; or at a temperature of 900.degree. C. to 1,100.degree. C. and with a water vapor content of 4% to 0.5%; then establishing the connection. The gas mixture for a treatment atmosphere is obtained by mixing nitrogen and hydrogen conducted through pipes (13, 14), to which oxygen is added through a pipe (15) upstream of a catalytic chamber (11) permitting the elimination of the oxygen and the production of a content of water vapor.