A process for preparing calcium sulphate comprising - producing dicalcium phosphate by • attacking in aqueous medium a phosphate source with an acid with the formation of a pulp comprising an aqueous phase containing watersoluble calcium phosphate and a solid phase containing impurities, • separating the aqueous phase, • neutralising the latter with a neutralizing calcium compound with precipitation of said dicalcium phosphate in an aqueous solution, and • isolating the precipitated dicalcium phosphate from this aqueous solution, and - digesting in an aqueous medium of isolated dicalcium phosphate by sulphuric acid under conditions resulting in the formation of a first slurry of calcium sulphate dihydrate crystals in suspension in an acidic aqueous phase having a free P 2 O 5 content, characterized in that the digestion is carried out at a temperature above 65°C and below 75°C, at a content of free P 2 O 5 in the acidic aqueous phase of 30-38% by weight of the first slurry and a content of free SO 3 in this acidic aqueous phase of more than 0.5% by weight of the first slurry and equal to or less than 1.5% by weight of the first slurry, and in that the process further comprises - converting at least a part of said first slurry by heating to a temperature above 80°C and optionally adding sulphuric acid, with solubilization of the calcium sulphate dihydrate crystals and recrystallization of the solubilized calcium sulphate resulting in a second slurry of α-type calcium sulphate hemihydrate crystals in suspension in an aqueous phase based on phosphoric acid, in which the content of free SO 3 is less than 10% by weight of the second slurry, and - separating in this second slurry, between the aqueous phase based on phosphoric acid and a filter cake based on α-type calcium sulphate hemihydrate. - producing dicalcium phosphate by • attacking in aqueous medium a phosphate source with an acid with the formation of a pulp comprising an aqueous phase containing watersoluble calcium phosphate and a solid phase containing impurities, • separating the aqueous phase, • neutralising the latter with a neutralizing calcium compound with precipitation of said dicalcium phosphate in an aqueous solution, and • isolating the precipitated dicalcium phosphate from this aqueous solution, and • attacking in aqueous medium a phosphate source with an acid with the formation of a pulp comprising an aqueous phase containing watersoluble calcium phosphate and a solid phase containing impurities, • separating the aqueous phase, • neutralising the latter with a neutralizing calcium compound with precipitation of said dicalcium phosphate in an aqueous solution, and • isolating the precipitated dicalcium phosphate from this aqueous solution, and - digesting in an aqueous medium of isolated dicalcium phosphate by sulphuric acid under conditions resulting in the formation of a first slurry of calcium sulphate dihydrate crystals in suspension in an acidic aqueous phase having a free P 2 O 5 content, - converting at least a part of said first slurry by heating to a temperature above 80°C and optionally adding sulphuric acid, with solubilization of the calcium sulphate dihydrate crystals and recrystallization of the solubilized calcium sulphate resulting in a second slurry of α-type calcium sulphate hemihydrate crystals in suspension in an aqueous phase based on phosphoric acid, in which the content of free SO 3 is less than 10% by weight of the second slurry, and - separating in this second slurry, between the aqueous phase based on phosphoric acid and a filter cake based on α-type calcium sulphate hemihydrate. <EOS>