A process for transforming a gas oil cut from a conversion process or from an aromatic crude is described, the aim of the process being to improve the cetane number of said cut. The process comprises at least one hydrogenation step in which said gas oil cut is passed, in the presence of hydrogen, over a catalyst comprising an amorphous mineral support, at least one compound of a group VIB metal, at least one compound of a non noble group VIII metal and at least phosphorous or a compound of phosphorous, the process then comprising a hydrocracking step in which the hydrogenated feed is passed, in the presence of hydrogen, over a catalyst comprising an acidic support, at least one compound of a group VIB metal and at least one compound of a non noble group VIII metal.