  We investigate baryogenesis via leptogenesis and generation of neutrino
masses and mixings through the Type I plus Type III seesaw plus an one-loop
mechanism in the context of Renormalizable Adjoint SU(5) theory. One light
neutrino remains massless, because the contributions of three heavy Majorana
fermions \rho_0, \rho_3 and \rho_8 to the neutrino mass matrix are not linearly
independent. However none of these heavy fermions is decoupled from the
generation of neutrino masses. This opens a new range in parameter space for
successful leptogenesis, in particular, allows for inverted hierarchy of the
neutrino masses.
