A method of manufacturing a composite material vane with a covering element, the vane including a platform and a profile extending perpendicularly to the platform, comprises the following steps: providing a covering element and a preform of the vane, the preform comprising a platform portion and a profile portion extending substantially perpendicularly to the platform portion; positioning the covering element against the platform portion so as to obtain an assembly; placing said assembly in a mold; injecting a first resin into the mold so that said resin impregnates and covers the preform and covers at least a portion of the covering element; and carrying out a heat treatment so as to harden the first resin.