  By means of a generalized quartet mechanism we show in a model independent
way that a BRST quantization on an inner product space leads to physical states
of the form |ph>=e^{[Q, \psi]} |ph>_0 where Q is the nilpotent BRST operator,
\psi a hermitian fermionic gauge fixing operator, and |ph>_0 BRST invariant
states determined by a hermitian set of BRST doublets in involution. |ph>_0
does not belong to an inner product space although |ph> does. Since the BRST
quartets are split into two sets of hermitian BRST doublets there are two
choices for |ph>_0 and the corresponding \psi. When applied to general, both
irreducible and reducible, gauge theories of arbitrary rank within the BFV
formulation we find that |ph>_0 are trivial BRST invariant states which only
depend on the matter variables for one set of solutions, and for the other set
|ph>_0 are solutions of a Dirac quantization. This generalizes previous Lie
group solutions obtained by means of a bigrading.
