  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.
