  We analyze the influence of different on-site and inter-site interactions on
the Curie temperature of transition metal magnetic elements. The numerical
calculations show the well known result that the on-site Coulomb repulsion
helps ferromagnetism mainly at half-filling of the band, where the 3d elements
are antiferromagnetic (Cr, Mn). The inter-site interactions, which in the new
approximation decrease the width of the band, favor ferromagnetism at both ends
of the band. At the same time they lower the ferromagnetic Curie temperature
towards experimental values, removing the paradox which persisted for a long
time.
