The process makes calcium sulfate alpha-hemihydrate or essentially plaster of paris from finely divided gypsum made by desulfurizing flue gas obtain from a power plant fired by brown coal by transforming the calcium sulfate dihydrate in the presence of saturated steam. A molded body is formed from the calcium sulfate dihydrate which has a plurality of pores. The pore volume amounts to 15 to 60% by volume of the total volume of the entire molded body. More than 5% by volume of the pore volume contains air. The molded body is fed to an autoclave. In the presence of a sufficient water quantity in the pores, the crystal habit and the crystal growth of the calcium sulfate alpha-hemihydrate crystals which grow in an aqueous solution phase are controlled by a process temperature in the range between 110.degree. to 180.degree. C. by the pressure of the treatment atmosphere in the autoclave. The molded body is removed from the autoclave after recrystallization transformation and delivered for use. Key products of this process and their derivatives are also described.