To inexpensively treat a fine powder such as a chlorine bypass dust containing chlorine and lead.

A slurry is generated by mixing the fine powder containing chlorine and lead, water, and a sulfiding agent. The slurry is separated into a solid content and a liquid content to obtain them, then the liquid content is evaporation-processed and the solid content is turned into a slurry to be subjected to a flotation process. Thanks to the evaporation process, facilities and chemicals for drainage treatment of the liquid content become unnecessary and thereby facilities and the operation cost can be saved. Furthermore, following merits are available. Wastewater generated in the flotation process can be beneficially used in a cement production facilities. It is possible that the solid content is turned into a slurry and the slurry is added with sulfuric acid and a collector to be subjected to the flotation process. An alkali agent is added to a drainage water generated by this to adjust its pH, then a part of a liquid content obtained by separating a tail product after the adjustment of a pH into a solid content and the liquid content, or a part of a drainage water obtained by separating this liquid content and a froth product into a solid content and a liquid content, can be used in the cement production facilities. A part or a whole of a residue after the evaporation process of the liquid content can be added to a cement until a chlorine concentration in the cement reaches an upper limit.