A process for the preparation of an alumina in the form of beads with a sulphur content in the range 0.001% to 1% by weight and a sodium content in the range 0.001% to 1% by weight with respect to the total mass of said beads is described, said beads being prepared by shaping an alumina gel having a high dispersibility by drop coagulation. The alumina gel is itself prepared using a specific precipitation preparation process in order to obtain at least 40% by weight of alumina with respect to the total quantity of alumina formed at the end of the gel preparation process right from the first precipitation step, the quantity of alumina formed at the end of the first precipitation step possibly even reaching 100%. The invention also concerns the use of alumina beads as a catalyst support in a catalytic reforming process.