Process for preparing an amorphous mesoporous alumina having a connectivity greater than 2.7, the connectivity being determined from nitrogen adsorption/desorption isotherms, the said process comprising at least the following steps: a) at least one first alumina precipitation step, in an aqueous reaction medium, of 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 precursor comprises aluminium, the relative flow rate of the acidic and basic precursors is chosen so as to obtain a pH of the reaction medium between 8.5 and 10.5, and the flow rate of the acidic and basic precursor or precursors containing aluminium is regulated so as to obtain a rate of progress of the said first step between 40 and 100%, the rate of progress being defined as the proportion of alumina formed as Al 2 O 3 equivalent during the first precipitation step with respect to the total amount of alumina formed at the end of the precipitation step or steps, the said first precipitation step being carried out at a temperature between 10 and 50°C and for a period between 2 minutes and 30 minutes, b) a heat treatment step of the suspension obtained at the end of the step a), at a temperature between 50 and 200°C for a period between 30 minutes and 5 hours, c) a filtration step of the suspension obtained at the end of the heat treatment step b), followed by at least one washing step of the obtained gel, d) a drying step of the alumina gel obtained at the end of the step c) so as to obtain a powder, e) a moulding step of the powder obtained at the end of the step d) so as to obtain the crude material, f) a heat treatment step of the crude material obtained at the end of the step e) at a temperature between 500 and 1000°C, in the presence or otherwise of a stream of air containing up to 60% by volume of water. a) at least one first alumina precipitation step, in an aqueous reaction medium, of 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 precursor comprises aluminium, the relative flow rate of the acidic and basic precursors is chosen so as to obtain a pH of the reaction medium between 8.5 and 10.5, and the flow rate of the acidic and basic precursor or precursors containing aluminium is regulated so as to obtain a rate of progress of the said first step between 40 and 100%, the rate of progress being defined as the proportion of alumina formed as Al 2 O 3 equivalent during the first precipitation step with respect to the total amount of alumina formed at the end of the precipitation step or steps, the said first precipitation step being carried out at a temperature between 10 and 50°C and for a period between 2 minutes and 30 minutes, b) a heat treatment step of the suspension obtained at the end of the step a), at a temperature between 50 and 200°C for a period between 30 minutes and 5 hours, c) a filtration step of the suspension obtained at the end of the heat treatment step b), followed by at least one washing step of the obtained gel, d) a drying step of the alumina gel obtained at the end of the step c) so as to obtain a powder, e) a moulding step of the powder obtained at the end of the step d) so as to obtain the crude material, f) a heat treatment step of the crude material obtained at the end of the step e) at a temperature between 500 and 1000°C, in the presence or otherwise of a stream of air containing up to 60% by volume of water.