  In the limit of infinite spatial dimensions a thermodynamically consistent
theory, which is valid for arbitrary value of the Coulombic interaction
($U<\infty$), is built for the Hubbard model when the total auxiliary
single-site problem exactly splits into four subspaces with different ``vacuum
states''. Some analytical results are given for the Hartree-Fock approximation
when the 4-pole structure for Green's function is obtained: two poles describe
contribution from the Fermi liquid component, which is ferromagnetic and
dominant for small electron and hole concentrations (``overdoped case'' of
high-$T_c$'s), whereas other two describe contribution from the non-Fermi
liquid, which is antiferromagnetic and dominant close to half filling
(``underdoped case'').
