  The BRST-anti-BRST covariant extension is suggested for the split involution
quantization scheme for the second class constrained theories. The constraint
algebra generating equations involve on equal footing a pair of BRST charges
for second class constraints and a pair of the respective anti-BRST charges.
Formalism displays explicit Sp(2) \times Sp(2) symmetry property. Surprisingly,
the the BRST-anti-BRST algebra must involve a central element, related to the
nonvanishing part of the constraint commutator and having no direct analogue in
a first class theory. The unitarizing Hamiltonian is fixed by the requirement
of the explicit BRST-anti-BRST symmetry with a much more restricted ambiguity
if compare to a first class theory or split involution second class case in the
nonsymmetric formulation. The general method construction is supplemented by
the explicit derivation of the extended BRST symmetry generators for several
examples of the second class theories, including self--dual nonabelian model
and massive Yang Mills theory.
