An exact macroscopic extended model, with many moments, for relativistic gases has been recently proposed in literature. However, a further condition, arising from the exploitation of the entropy principle, has not been imposed, even if its presence is evident in the case of a charged gas and when the electromagnetic field acts as an external force. In the present paper we exploit it and we prove that it amounts in many identities plus some residual conditions which allow to determine the arbitrary single variable functions present in the general theory. The result is that they are polynomials of increasing degree with respect to equilibrium, which coefficients are arbitrary constants. Even in such case the macroscopic model remains more general than the kinetic one
