An installation for producing bead wires intended for the reinforcement of a tire, such as a pneumatic tire, said installation comprising a braiding station which comprises a guiding support which defines a path which follows a generatrix line which is closed in a ring on itself about a main axis, a reel arranged to bring a braid wire preferably metallic, and to cooperate with the guiding support in order to wind said braid wire in helical turns about, and along, said generatrix line so as to form, through a plurality of turns about said main axis, a braided torus that includes a bead wire element, the braid wire having a winding section that includes a portion of length which corresponds to the helical turns and which occupies a braid volume, and the braid wire also including an excess section that is an extension of said winding section which includes a surplus length of braid wire, wherein the installation also comprises a folding tool, distinct with respect to the reel, and arranged to recover, after the braiding operation, the excess section and perform a plastic folding of said excess section so as to form an elbow which makes the excess section diverge with respect to the helical turns and makes said excess section protrude at least partly with respect to the braid volume of the braided torus.