Recently a model, which is equivalent to the scalar form of a Gursey model, is shown to be a nontrivial field theoretical model when it is gauged with a SU(N) field. In this paper we study another model that is equivalent to the vector form of the Gursey model. We get a trivial theory when it is coupled with a scalar field. This result changes drastically when it is coupled with an additional SU(N) field. We find a nontrivial field theoretical model under certain conditions.