It is shown that in the first order gauge theories under some general
assumptions gauge conditions can play the role of new local symmetry
generators, while the original constraints become gauge fixing terms. It is
possible to associate with this new symmetry a second BRST charge and its
anticommutator with the original BRST charge is the Hodge operator of the
corresponding cohomology complex.Comment: 7 pages, LaTeX, some changes in the BRST sectio