  We show that, in the framework of covariant Hamiltonian field theory, a
degenerate almost regular quadratic Lagrangian $L$ admits a complete set of
non-degenerate Hamiltonian forms such that solutions of the corresponding
Hamilton equations, which live in the Lagrangian constraint space, exhaust
solutions of the Euler--Lagrange equations for $L$. We obtain the
characteristic splittings of the configuration and momentum phase bundles. Due
to the corresponding projection operators, the Koszul-Tate resolution of the
Lagrangian constraints for a generic almost regular quadratic Lagrangian is
constructed in an explicit form.
