  We complete the formulation of the equations of motion of a non-Abelian gauge
field coupled to fermions on a finite-element lattice in four space-time
dimensions. This is accomplished by a straightforward iterative approach, in
which successive interaction terms are added to the Dirac and Yang-Mills
equations of motion, and to the field strength, in order to preserve lattice
gauge invariance exactly, yielding a series in powers of $ghA$. Here $g$ is the
coupling constant, $h$ is the lattice spacing, and $A$ is the gauge potential.
Gauge transformations of the potentials are determined simultaneously. The
interaction terms in the equations of motion are nonlocal, and can be expressed
either by an iterative formula or by a difference equation. On the other hand,
the field strength is locally constructed from the potentials in terms of a
path-ordered product of exponentials.
