Cutting device for cutting a reinforcing ply (N) formed of a set of portions of thread, of given length, coated in a rubber compound, laid parallel to one another and making a given theoretical angle (a) with the longitudinal direction of the ply, characterized in that it includes a first element able, without proceeding to cut the said ply (N), to estimate the actual angle of the threads with the longitudinal direction (XX′) of the device and a second element able to cut the ply (N) at the actual angle (a+da) estimated by the first element.