  We construct the order alpha'^3 terms in the supersymmetric Yang-Mills action
in ten dimensions for an arbitrary gauge group. The result can be expressed in
terms of the structure constants of the Yang-Mills group, and is therefore
independent of abelian factors. The alpha'^3 invariant obtained here is
independent of the alpha'^2 invariant, and we argue that additional
superinvariants will occur at all odd orders of alpha'.
