  An exact analytical diagonalization is used to solve the two dimensional
Extended Hubbard Model for system with finite size. We have considered an
Extended Hubbard Model (EHM) including on-site and off-site interactions with
interaction energy U and V respectively, for square lattice containing 4*4
sites at one-eighth filling with periodic boundary conditions, recently treated
by Kovacs et al [1]. Taking into account the symmetry properties of this square
lattice and using a translation linear operator, we have constructed a r-space
basis, only, with 85 state-vectors which describe all possible distributions
for four electrons in the 4*4 square lattice. The diagonalization of the 85*85
matrix energy allows us to study the local properties of the above system as
function of the on-site and off-site interactions energies, where, we have
shown that the off-site interaction encourages the existence of the double
occupancies at the first exited state and induces supplementary conductivity of
the system.
