Abstract The thermodynamic potential for nuclear matter is calculated in the 1/ N expansion of the relativistic σ-ω model. The relativistic exchange and correlation parts, which are included in the next-to-leading-order terms, are calculated at finite temperature for all thermodynamic observables. The thermodynamic consistency of the 1/ N expansion is verified in the context of thermo field dynamics and the imaginary-time path-integral formalism. The equation of state (EOS) of nuclear matter at finite density and temperature is investigated and the various contributions to the thermodynamic observables are discussed. It is emphasized that the inclusion of the higher-order terms leads to a softening of the EOS, which is important in view of empirical information from heavy-ion collisions and astrophysics.