Process for hydrotreatment of at least one hydrocarbon feedstock having a weighted average temperature of more than 380°C operating at a temperature of between 250°C and 430°C, at a total pressure of between 4 MPa and 20 MPa with a ratio of volume of hydrogen to volume of hydrocarbon feedstock of between 200 and 2 000 litres per litre and at an Hourly Volume Velocity defined by the ratio of the volume flow of liquid hydrocarbon feedstock to the volume of catalyst fed into the reactor of between 0.5 and 5 h-1, said process using at least one catalyst containing at least one metal from Group VIB and/or at least one metal from Group VIII of the periodic table and a support containing an amorphous mesoporous alumina, said process comprising at least the following steps of preparation of said alumina: a) at least one first step a) of alumina precipitation, in aqueous reaction medium, of at least one basic precursor selected from among sodium aluminate, potassium aluminate, ammonia, sodium hydroxide and potassium hydroxide and at least one acid precursor selected from among aluminium sulphate, aluminium chloride, aluminium nitrate, sulphuric acid, hydrochloric acid, and nitric acid, wherein at least one of the basic or acid precursors comprises aluminium, the relative flow of the acid and basic precursors is selected in order to obtain a pH of the reaction medium of between 8.5 and 10.5 and the flow of the acid and basic precursor(s) containing aluminium is adjusted in order to obtain a rate of progress of the first step of between 40 and 100%, the rate of progress being defined as being the alumina formed as equivalent Al 2 O 3 in said precipitation step a) as a proportion of the total quantity of alumina formed in the precipitation step(s), said step a) operating at a temperature of between 10 and 50 °C, and for a period of between 2 minutes and 30 minutes, b) a step for thermal treatment of the suspension obtained in step a) at a temperature of between 50 and 200°C for a period of between 30 minutes and 5 hours, c) a step for filtration of the suspension obtained from thermal treatment step b), followed by at least one washing step of the gel obtained, d) a step for drying the alumina gel obtained in step c) for obtaining a powder, e) a step for shaping the powder obtained in step d) for obtaining the raw material, f) a step for thermal treatment of the raw material obtained in step e) at a temperature of between 500 and 1 000°C, in the presence or not of an air flow containing up to 60 vol.% of water. a) at least one first step a) of alumina precipitation, in aqueous reaction medium, of at least one basic precursor selected from among sodium aluminate, potassium aluminate, ammonia, sodium hydroxide and potassium hydroxide and at least one acid precursor selected from among aluminium sulphate, aluminium chloride, aluminium nitrate, sulphuric acid, hydrochloric acid, and nitric acid, wherein at least one of the basic or acid precursors comprises aluminium, the relative flow of the acid and basic precursors is selected in order to obtain a pH of the reaction medium of between 8.5 and 10.5 and the flow of the acid and basic precursor(s) containing aluminium is adjusted in order to obtain a rate of progress of the first step of between 40 and 100%, the rate of progress being defined as being the alumina formed as equivalent Al 2 O 3 in said precipitation step a) as a proportion of the total quantity of alumina formed in the precipitation step(s), said step a) operating at a temperature of between 10 and 50 °C, and for a period of between 2 minutes and 30 minutes, b) a step for thermal treatment of the suspension obtained in step a) at a temperature of between 50 and 200°C for a period of between 30 minutes and 5 hours, c) a step for filtration of the suspension obtained from thermal treatment step b), followed by at least one washing step of the gel obtained, d) a step for drying the alumina gel obtained in step c) for obtaining a powder, e) a step for shaping the powder obtained in step d) for obtaining the raw material, f) a step for thermal treatment of the raw material obtained in step e) at a temperature of between 500 and 1 000°C, in the presence or not of an air flow containing up to 60 vol.% of water.