  We consider Yang-Mills theory in Euclidean space-time $(R^4)$ and construct
its configuration space. The orbits are first shown to form a congruence set.
Then we discuss the orthogonal gauge condition in Abelian theory and show that
Coulomb-like surfaces foliate the entire configuration space. In the
non-Abelian case, where these exists no global orthogonal gauge, we derive the
non-linear gauge proposed previously by the author by modifying the
orthogonality condition. However, unlike the Abelian case, the entire
configuration space cannot be foliated by submanifolds defined by the
non-linear gauge. The foliation is only limited to the non-perturbative regime
of Yang-Mills theory.
