A method of producing an alloy containing at least one major ingredient selected from the group consisting of iron (Fe), cobalt (Co), and Nickel (Ni) and having low contents of sulphur, oxygen, and nitrogen, comprises steps of:(a) holding a molten alloy in a container selected from the group consisting of a lime crucible, a lime crucible furnace, a converter and a ladle lined with a basic refractory consisting of 15-85% of calcium oxide (CaO), and 15-75% of magnesium oxide (MgO), wherein said alloy consists essentially of at least one major ingredient selected from the group consisting of iron (Fe), nickel (Ni), and cobalt (Co);(b) adding at least one additive, based on the molten alloy, into said molten alloy in an atmosphere selected from the group consisting of a non-oxidizing atmosphere and a vacuum, wherein said additive is selected from the group consisting of aluminum (Al), aluminum alloys, silicon and silicon alloys;(c) desulphurizing, deoxidizing and denitrifying said molten alloy under an atmosphere selected from the group consisting of a non-oxidizing atmosphere and a vacuum, whereby the molten alloy contains 0.005 to 7.0% of residual aluminum, 0.0001 to 0.02% of residual calcium, and 0.0005 to 0.03% of residual magnesium; and(d) casting said molten alloy into a mold.