According to the process, limestone is burned at a high temperature to form calcium oxide and, thereafter, calcium carbonate is formed from calcium oxide in the presence of water and carbonate ions and the formed calcium carbonate is recovered. The formation of the carbonate may be performed by carbonating calcium oxide with carbon dioxide gas in the presence of water or water vapour, or by reacting calcium oxide with soda solution. According to the invention calcium oxide is converted to calcium carbonate without separate slaking and essentially without intermediate storage, in particular without intermediate storage between the burning of the starting material and the forming of calcium carbonate. With the aid of the invention a quite advantageous solution in view of heat economy is achieved.