[en] We formulate the helicity amplitudes for multiple bremsstrahlung processes in massless gauge theories in terms of spinor inner-products. In the non-abelian case (QCD) we show that contributions from the diagrams with gluon self-coupling can be decomposed into parts to be included together with QED-like diagrams in gauge-invariant subsets, and the amplitudes of the parts are related to the amplitudes of QED-like diagrams. This enables us to make use of the simplifying power of the helicity amplitude method as far as possible. (orig.)