A natural generalized symmetry of the Yang–Mills equations is defined as an infinitesimal transformation of the Yang–Mills field, built in a local, gauge invariant, and Poincaré invariant fashion from the Yang–Mills field strength and its derivatives to any order, which maps solutions of the field equations to other solutions. On the jet bundle of Yang–Mills connections a spinorial coordinate system is introduced that is adapted to the solution subspace defined by the Yang–Mills equations. In terms of this coordinate system the complete classification of natural symmetries is carried out in a straightforward manner. It is found that all natural symmetries of the Yang–Mills equations stem from the gauge transformations admitted by the equations.