In this paper, at first we formulate the lowest order constrained variational method for the relativistic case of an interacting fermion system at finite temperature. Then, we used this formalism to calculate some thermodynamic properties of liquid 3 He in the relativistic regime. The results show that the difference between total energies of the relativistic and non-relativistic cases of liquid 3 He decreases by increasing the density. On the other hand, at densities smaller than ρ = 0.010 Å

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... , which is close to the theoretical saturation point of the system, this difference increases as the temperature increases. We also found that the relativistic calculations lead to the thermodynamic characteristics for liquid 3 He which are in a better agreement with the experimental data with respect to those of non-relativistic calculations.