  Using a separable many-body variational wavefunction, we formulate a
self-consistent effective Hamiltonian theory for fermionic many-body system.
The theory is applied to the two-dimensional Hubbard model as an example to
demonstrate its capability and computational effectiveness. Most remarkably for
the Hubbard model in 2-d, a highly unconventional quadruple-fermion
non-Cooper-pair order parameter is discovered.
