A method for preparing calcium sulphate comprising a production of DCP by the attack of a source of phosphate by an acid, a digestion of the isolated DCP by the sulphuric acid under conditions giving rise to the formation of a first slurry of gypsum suspended in an acidic aqueous phase having a content of free SO3 equal to or less than 1.5% and a content of free P2O5, a conversion of at least part of said first slurry by heating to a temperature greater than 80° C. and potentially by adding sulphuric acid, with solubilisation of the gypsum crystals and recrystallisation of the solubilised calcium sulphate in a second slurry of α-calcium sulphate hemihydrate crystals suspended in an aqueous phase based-on phosphoric acid, wherein the content of free SO3 is less than 10% by weight, and a separation between said aqueous phase and a filter cake based on particularly pure α-calcium sulphate hemihydrate.