PURPOSE: To eliminate the necessity for producing 'a fabric' of a kind made up by interlacing warp thread and bundling thread and to ensure the mechanical soundness of a reinforcement.

CONSTITUTION: A reinforcement in the form of a sheet for a composite element contains superposed plies 2, 3 of thread and the straight portions 4, 5 of thread are arranged, for each ply, at least substantially in a parallel fasion with respect to each other and all the superposed plies are consolidated by using a thread passing through the plies. The superposed plies 2, 3 are laid down on supports 6A, 6B and compacted by mechanical pressure and, in order to preserve the state of compaction of the piles, the thread F for consolidating the plies 2, 3 is stitched, without knotting, through the plies down to at least the level of the surfaces of the supports 6A, 6B. The plies have, after compaction, a density of the portions of the thread constituting them which is sufficient to retain the consolidating thread by friction.