In order to make labyrinth seal lips on the periphery of a metal moving part of a turbomachine, a thick layer of refractory material that adheres to the metal is made prior to assembling the moving part, the refractory material advantageously comprising at least one metal selected for example from Fe, Co, and Ni, together with at least one ceramic selected for example from borides, nitrides, carbides, and refractory oxides. The labyrinth seal lips that are to be made are machined to their final dimensions in the deposited thick layer.