Alunite was dehydrated at 500~$580^{circ}C$ and desulfurued at 580~$780^{circ}C$ in air atmosphere. Therefore, this study was carried out to investigate the formation conditions of anhydrite ($CaCO_4$) when the mixtures of alunite TEX>$[K_2SO_4$</TEX>.$Al_2(SO_4)_3$.$4Al(OH)_3$] and limestone ($CaCO_3$)were roasted. Alunite scarcely dected the partial pressures of $CO_2$(g), but limestone was bansformed into CaO at $650^{circ}C$ in air and $900^{circ}C$ in saturated $CO_2$(g), atmosphere, respectively. When the the mixtures of 1 mol of alunite and 6 rnol of limestone were roasted for 2 hours at lO00C in air and saturated $CO_2$(g), anhydrite was formed at $550^{circ}C$ calciumlangbeinite, at $700^{circ}C$and haiiyne, at 800~$950^{circ}C$. The formation rate of anhydrite in air and saturated $CO_2$(g), was 99.0 % and 95.0 %, respectively. then the formation rate of anhydrite was not changed in air atmosphere but increased according to the decreasing of the particle size of limestone in saturated $CO_2$(g). Therefore, when the mixture of 1 mol of alunite and 6 rnol of limestone were roasted, the clinker composed of lmol of haiiync and 1 mol of calciumlangbeiilte can be manufactured