  We propose a modified version of the Faddeev-Popov quantization approach for
non-Abelian gauge field theory to avoid the Gribov ambiguity. We show that by
means of introducing a new method to insert the correct identity into the
Yang-Mills generating functional and considering the identity generated by an
integral through a subgroup of the gauge group, the problem of the Gribov
ambiguity can be removed naturally. Meanwhile by handling the absolute value of
the Faddeev-Popov determinant with the method introduced by Williams and
collaborators, we lift the Jacobian determinant together with the absolute
value and obtain a local Lagrangian. The new Lagrangian have a nilpotent
symmetry which can be viewed as an analogue of the BRST symmetry.
