  The influence of next-nearest neighbor electron hopping, $t^{\prime}$, on the
polaron and bipolaron formation in a square Hubbard-Holstein model is
investigated within a variational approach. The results for electron-phonon and
electron-electron correlation functions show that a negative value of
$t^{\prime}$ induces a strong anisotropy in the lattice distortions favoring
the formation of nearest neighbor intersite bipolaron. The role of
$t^{\prime}$, electron-phonon and electron-electron interactions is briefly
discussed in view of the formation of charged striped domains.
