Class of ghost-free non-Abelian gauge theories

We discuss a class of non-Abelian gauge theories characterized by the gauge condition ${\Lambda }_{\mu }{W}_{\mu }^a=h^a$, where ${\Lambda }_{\mu }$ is an arbitrary four-vector and $h^a$ denotes a set of arbitrary functions. We show that this class of theories is ghost free. Using the method of gauge variation of proper vertices, we prove that the $S$-matrix elements are independent of the gauge parameter ${\Lambda }_{\mu }$.