We expand the gauge field in terms of a suitably constructed complete set of Bloch wave functions, each labeled by a band designation $n$ and a wave number $\stackrel{\ensuremath{\rightarrow}}{K}$ restricted to the Brillouin zone. A noncompact formulation of lattice QCD (or QED) can be derived by restricting the expansion only to the zeroth-band ($n=0$) functions, which are simple continuum interpolations of discrete values associated with sites or links on a lattice. The exact continuum theory can be reached through the inclusion of all $n=0$ and $n\ensuremath{\ne}0$ bands, without requiring the lattice size $l\ensuremath{\rightarrow}0$. This makes it possible, at a nonzero $l$, for the lattice coupling ${g}_{l}$ to act as the renormalized continuum coupling. All physical results in the continuum are, of course, independent of $l$.