the present invention relates to a method of fabricating a rod of composite material from a fiber preform comprising a certain number of primary fiber plies connected together by links allowing plies to slide relative to one another while the preform is being shaped , the preform including a central portion for constituting the body of the rod and including two opposite side portions , together with extensions for forming lugs of the rod , which method includes the step of shaping the fiber preform so as to give it a hollow shape while keeping the two opposite side portions spaced apart so as to give the fiber preform an open profile in its central portion , followed by injecting resin and causing it to polymerize .