  The Loop Variable method that has been developed for the U(1) bosonic open
string is generalized to include non-Abelian gauge invariance by incorporating
"Chan-Paton" gauge group indices. The scale transformation symmetry $k(s) \to
k(s) \lambda (s)$ that was responsible for gauge invariance in the U(1) case
continues to be a symmetry. In addition there is a "rotation" symmetry. Both
symmetries crucially involve the massive modes. However it is plausible that
only a linear combination, which is the usual Yang-Mills transformation on
massless fields, has a smooth (world sheet) continuum limit. We also illustrate
how an infinite number of terms in the equation of motion in the cutoff theory
add up to give a term that has a smooth continuum limit, and thus contributes
to the low energy Yang-Mills equation of motion.
