  Recently, the explicit evaluation of Gauss sums in the index 2 and 4 cases
have been given in several papers (see [2,3,7,8]). In the course of evaluation,
the sigh (or unit root) ambiguities are unavoidably occurred. This paper
presents another method, different from [7] and [8], to determine the sigh
(unit root) ambiguities of Gauss sums in the index 2 case, as well as the ones
with odd order in the non-cyclic index 4 case. And we note that the method in
this paper are more succinct and effective than [8] and [7].
