A method for combustion of a carbon-containing fuel, especially a fossil fuel, further preferred coal. The flue gas is at least dedusted, is desulfurized with an absorbent containing calcium compounds, and in a two-stage high temperature process is decarbonized with calcium oxide in a carbonator accompanied by formation of calcium carbonate and the calcium carbonate is regenerated in a calcinator, while heat is supplied and while carbon dioxide is set free, to form calcium oxide, which is recirculated into the carbonator. At least to one of the stages of the high temperature process fresh calcium containing absorbent is added. Calcium compounds from the carbonator and/or calcinator are used as absorbent with the flue gas desulfurization.