  We propose an extended BRST invariant Lagrangian quantization scheme of
general gauge theories based on an explicit realization of the modified
triplectic algebra that was announced in our previous investigation
(hep-th/0104189). The algebra includes, besides the odd operators $V^a$
appearing in the triplectic formalism, also the odd operators $U^a$ introduced
within modified triplectic quantization, both of which being anti-Hamiltonian
vector fields. We show that some even supersymplectic structure defined on the
space of fields and antifields provides the extended BRST path integral with a
well-defined integration measure. All the known Lagrangian quantization schemes
based on the extended BRST symmetry are obtained by specifying the (free)
parameters of that method.
