Split Involution Coupled to Actual Gauge Symmetry

The split involution quantization scheme, proposed previously for pure second--class constraints only, is extended to cover the case of the presence of irreducible first--class constraints. The explicit Sp(2)--symmetry property of the formalism is retained to hold. The constraint algebra generating equations are formulated and the Unitarizing Hamiltonian is constructed. Physical operators and states are defined in the sense of the new equivalence criterion that is a natural counterpart to the Dirac's weak equality concept as applied to the first--class quantities.