A process for the preparation of an alumina in the form of beads with a sulphur content of between 0.001% and 1% by weight and a sodium content of between 0.001% and 1% by weight with respect to the total mass of said beads, said process comprising at least the following steps: a) at least one first step for the precipitation of alumina, in an aqueous reaction medium, using at least one basic precursor selected from sodium aluminate, potassium aluminate, ammonia, sodium hydroxide and potassium hydroxide and at least one acidic precursor selected from aluminium sulphate, aluminium chloride, aluminium nitrate, sulphuric acid, hydrochloric acid and nitric acid, in which at least one of the basic or acidic precursors comprises aluminium, the relative flow rate of the acidic and basic precursors being selected in a manner such as to obtain a pH of the reaction medium of between 8.5 and 10.5 and the flow rate of the acidic and basic precursor or precursors containing aluminium being regulated in a manner such as to obtain a percentage completion of said first step of between 40% and 100%, the percentage completion being defined as being the proportion of alumina formed in equivalents of Al 2 O 3 during said first precipitation step with respect to the total quantity of alumina formed at the end of the precipitation step or steps, said first precipitation step being operated at a temperature of between 10°C and 50°C, and for a period of between 2 minutes and 30 minutes; b) a step for heat treatment of the suspension obtained at the end of step a) at a temperature of between 50°C and 200°C for a period of between 30 minutes and 5 hours in order to obtain an alumina gel; c) a step for filtration of the suspension obtained at the end of the heat treatment step b) followed by at least one step for washing the gel obtained; d) a step for drying the alumina gel obtained at the end of step c) in order to obtain a powder; e) a step for shaping the powder obtained at the end of step d) by drop coagulation in order to obtain the crude material; f) a step for heat treatment of the crude material obtained at the end of step e) at a temperature of between 500°C and 1000°C, in the presence or absence of a stream of air containing up to 60% by volume of water. a) at least one first step for the precipitation of alumina, in an aqueous reaction medium, using at least one basic precursor selected from sodium aluminate, potassium aluminate, ammonia, sodium hydroxide and potassium hydroxide and at least one acidic precursor selected from aluminium sulphate, aluminium chloride, aluminium nitrate, sulphuric acid, hydrochloric acid and nitric acid, in which at least one of the basic or acidic precursors comprises aluminium, the relative flow rate of the acidic and basic precursors being selected in a manner such as to obtain a pH of the reaction medium of between 8.5 and 10.5 and the flow rate of the acidic and basic precursor or precursors containing aluminium being regulated in a manner such as to obtain a percentage completion of said first step of between 40% and 100%, the percentage completion being defined as being the proportion of alumina formed in equivalents of Al 2 O 3 during said first precipitation step with respect to the total quantity of alumina formed at the end of the precipitation step or steps, said first precipitation step being operated at a temperature of between 10°C and 50°C, and for a period of between 2 minutes and 30 minutes; b) a step for heat treatment of the suspension obtained at the end of step a) at a temperature of between 50°C and 200°C for a period of between 30 minutes and 5 hours in order to obtain an alumina gel; c) a step for filtration of the suspension obtained at the end of the heat treatment step b) followed by at least one step for washing the gel obtained; d) a step for drying the alumina gel obtained at the end of step c) in order to obtain a powder; e) a step for shaping the powder obtained at the end of step d) by drop coagulation in order to obtain the crude material; f) a step for heat treatment of the crude material obtained at the end of step e) at a temperature of between 500°C and 1000°C, in the presence or absence of a stream of air containing up to 60% by volume of water.