The present invention concerns the down hole motors used in the oil prospecting industry to drive drill bits for drilling the ground at great depths. The down hole motor (1) comprises a drive shaft (5) held in the motor body (3) by an axial thrust bearing (6) and by a radial bearing (7). The radial bearing (7) is a tubular member whose interior surface is coated with an anti-abrasion layer (11) formed by laser-assisted facing directly inside an alloy steel radial bearing body (10). The thickness of the facing layer is then reduced by removing material by means of a cutting tool.This produces a radial bearing (7) that is relatively insensitive to drilling mud and confers great reliability on the down hole motor (1).