  In this contribution we would like to revisit the problems of ferromagnetism
(F) and antiferromagnetism (AF) in the pure itinerant model. These methods can
be extended later to the superconducting materials. In our model we assume the
extended Hubbard Hamiltonian. Transition from the paramagnetic state to the
ordered state of magnetic nature is decided by the competition between kinetic
and potential energy in which there is an increase in the kinetic energy
moderated by the inter-site interactions, and a decrease in the potential
energy. The competition between these two energies results in the existence of
critical values of interactions for creating magnetic alignment. Only when
existing in a given material interaction exceeds the critical value for a given
type of ordering we can have the alignment of this type.
  The influence of inter-site correlation on F and AF in the presence of
Coulomb on-site correlation is investigated. The well known Landau free energy
expansion is corrected for both F and AF ordering to reflect the presence of
critical interaction in the second order term, which leads to the magnetic
alignment.
  The numerical results show that the inter-site interactions favor F at the
end of the band and AF at the half-filled point. In both cases of F and AF
ordering, these interactions lower substantially the Curie and Neel's
temperature towards experimental data. This helps to remove the paradox in
magnetism that has persisted for a long time.
