In the absence of Gribov complications, the modified gauge fixing in gauge theory $ \int{\cal D}A_��\{\exp[-S_{YM}(A_��)-\int f(A_��)dx] /\int{\cal D}g\exp[-\int f(A_��^{g})dx]\}$ for example, $f(A_��)=(1/2)(A_��)^{2}$, is identical to the conventional Faddeev-Popov formula $\int{\cal D}A_��\{��(D^��\frac{��f(A_��)}{��A_��})/\int {\cal D}g��(D^��\frac{��f(A_��^{g})} {��A_��^{g}})\}\exp[-S_{YM}(A_��)]$ 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.

12 pages