Recently we have proposed a renormalizable grand unified theory, based on the SU(5) gauge symmetry, where the neutrino masses are generated through the type I and type III seesaw mechanisms. In this letter we study the supersymmetric version of this theory. As in the non-susy version it is possible to generate all fermion masses with the minimal number of Higgses, the theory predicts one massless neutrino and the leptogenesis mechanism can be realized. All contributions to the decay of the

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... n and the properties of neutralinos are discussed. This theory can be considered as the simplest renormalizable supersymmetric grand unified theory based on the SU(5) gauge symmetry since it has the minimal number of superfields and free parameters.