A process for the treatment of a hydrocarbon feed containing at least one hydrocarbon fraction having a sulphur content of at least 0.1% by weight, an initial boiling point of at least 340°C and a final boiling point of at least 440°C, said process comprising the following steps: a) a fixed bed hydrotreatment step, in which the hydrocarbon feed and hydrogen are brought into contact over a hydrotreatment catalyst; b) an optional step of separating the effluent obtained from the hydrotreatment step a) into at least one light hydrocarbon fraction containing fuel bases and a heavy fraction containing compounds boiling at at least 350°C, c) a step of hydrocracking at least a portion of the effluent obtained from step a) or at least a portion of the heavy fraction obtained from step b) in at least one ebullated bed reactor containing a supported catalyst, d) a step of separating the effluent obtained from step c) in order to obtain at least one gaseous fraction and at least one heavy liquid fraction, e) a step of precipitating sediment, in which the heavy liquid fraction obtained from the separation step d) is brought into contact with a distillate cut wherein at least 20% by weight has a boiling point of 100°C or more, for a period of less than 500 minutes, at a temperature in the range 25°C to 350°C, and a pressure of less than 20 MPa, f) a step of physical separation of the sediments from the heavy liquid fraction obtained from the precipitation step e) in order to obtain a liquid hydrocarbon fraction, g) a step of recovering a liquid hydrocarbon fraction having a sediment content, measured in accordance with the ISO 10307-2 method, of 0.1% by weight or less, consisting of separating the liquid hydrocarbon fraction obtained from step f) from the distillate cut introduced during step e). a) a fixed bed hydrotreatment step, in which the hydrocarbon feed and hydrogen are brought into contact over a hydrotreatment catalyst; b) an optional step of separating the effluent obtained from the hydrotreatment step a) into at least one light hydrocarbon fraction containing fuel bases and a heavy fraction containing compounds boiling at at least 350°C, c) a step of hydrocracking at least a portion of the effluent obtained from step a) or at least a portion of the heavy fraction obtained from step b) in at least one ebullated bed reactor containing a supported catalyst, d) a step of separating the effluent obtained from step c) in order to obtain at least one gaseous fraction and at least one heavy liquid fraction, e) a step of precipitating sediment, in which the heavy liquid fraction obtained from the separation step d) is brought into contact with a distillate cut wherein at least 20% by weight has a boiling point of 100°C or more, for a period of less than 500 minutes, at a temperature in the range 25°C to 350°C, and a pressure of less than 20 MPa, f) a step of physical separation of the sediments from the heavy liquid fraction obtained from the precipitation step e) in order to obtain a liquid hydrocarbon fraction, g) a step of recovering a liquid hydrocarbon fraction having a sediment content, measured in accordance with the ISO 10307-2 method, of 0.1% by weight or less, consisting of separating the liquid hydrocarbon fraction obtained from step f) from the distillate cut introduced during step e).