  I apply a two-step density-matrix renormalization group method to the
anisotropic two-dimensional Hubbard model. As a prelude to this study, I
compare the numerical results to the exact one for the tight-binding model. I
find a ground-state energy which agrees with the exact value up to four digits
for systems as large as $24 \times 25$. I then apply the method to the
interacting case. I find that for strong Hubbard interaction, the ground-state
is dominated by magnetic correlations.
  These correlations are robust even in the presence of strong frustration.
Interchain pair tunneling is negligible in the singlet and triplet channels and
it is not enhanced by frustration. For weak Hubbard couplings, interchain
non-local singlet pair tunneling is enhanced and magnetic correlations are
strongly reduced. This suggests a possible superconductive ground state.
