The invention relates to a process for preparing middle distillates from a paraffinic feedstock produced by Fischer-Tropsch synthesis, using a hydrocracking/hydroisomerization catalyst which comprises at least one hydrodehydrogenating element chosen from the group formed by the noble elements of Group VIII of the periodic table, a silica-alumina-based non-zeolitic support obtained from wherein the non-zeolitic silica-alumina based support was obtained from a process comprising starting from a mixture of a partially soluble alumina compound in an acid medium with a totally soluble silica compound or with a totally soluble combination of alumina and hydrated silica, the resultant moldable mixture is concentrated to form a moldable mixture, the resultant mixture is molded and the resultant molded article is subjected to a hydrothermal or thermal treatment.