  In the absence of Gribov complications, the modified gauge fixing in gauge
theory $ \int{\cal D}A_{\mu}\{\exp[-S_{YM}(A_{\mu})-\int f(A_{\mu})dx]
/\int{\cal D}g\exp[-\int f(A_{\mu}^{g})dx]\}$ for example,
$f(A_{\mu})=(1/2)(A_{\mu})^{2}$, is identical to the conventional Faddeev-Popov
formula $\int{\cal D}A_{\mu}\{\delta(D^{\mu}\frac{\delta f(A_{\nu})}{\delta
A_{\mu}})/\int {\cal D}g\delta(D^{\mu}\frac{\delta f(A_{\nu}^{g})} {\delta
A_{\mu}^{g}})\}\exp[-S_{YM}(A_{\mu})]$ if one takes into account the variation
of the gauge field along the entire gauge orbit. Despite of its quite different
appearance,the modified formula defines a local and BRST invariant theory and
thus ensures unitarity at least in perturbation theory. In the presence of
Gribov complications, as is expected in non-perturbative Yang-Mills theory, the
modified formula is equivalent to the conventional formula but not identical to
it:Both of the definitions give rise to non-local theory in general and thus
the unitarity is not obvious. Implications of the present analysis on the
lattice regularization are briefly discussed.
