Method and system for a cement burning facility. When exhaust gas in a part of a preheater or a kiln inlet of a cement kiln is extracted, a cement material is dispersed. The dispersed amount of the cement material is adjusted to maintain the temperature of the extracted gas between 950° C. and 1,150° C. The extracted gas is cooled to at most the melting point of a chlorine compound. A solid-gas separation device adjusts classification particle size to between 15 μm and 30 μm. A dust trap removes fine powder dust with a particle size equal to or smaller than the classification particle size. The amount of fine powder dust collected by the dust trap is maintained between 50 g/m3N and 150 g/m3N, with the concentration of chlorine in the collected fine powder dust set to between 5% and 20%.