the invention relates to a method for manufacturing an arm in composite material , this arm comprising a main body incorporating a bearing designed to receive a shaft passing through it transversely , this method comprising the steps of : manufacturing a hub by winding reinforcing fibers around a generally tubular support ; manufacturing at least one sleeve ; attaching the hub to one end of the sleeve and transversely to the sleeve in order to form a mandrel ; applying one or more layers of braided reinforcing fibers around this mandrel with a machine for braiding reinforcing fibers ; injecting and polymerizing resin into the layer or layers of braided fibers . the invention applies notably to an arm forming an undercarriage rocker arm of an aircraft .