The fumes from gas turbine TG are cooled by heat exchangers E1, E2, E01, E02 and E03 and compressed by compressors C1 and C2. The cold and high-pressure fumes are depleted in carbon dioxide in treating plant 10. The fumes depleted in carbon dioxide are heated by heat exchangers E1 and E2, and expanded by turbines T2, then T1. The energy recovered in form of heat in exchangers E01, E02 and E03 is converted into mechanical energy by the engine cycle used by turbine T, condenser E and pump P. The mechanical energy is available at the shaft of turbine T.