In this paper, we present a nonperturbative method of calculating the nonequilibrium partition function appearing in the nonequilibrium ensemble method for dilute gases. A set of first-order partial differential equations is derived for the nonequilibrium partition function. The set can be put into an exact differential form and its integral gives the nonequilibrium partition function with which various macroscopic variables can be expressed. In particular, on solving the aforementioned partial differential equations for the derivatives, the nonequilibrium constitutive relations are directly obtained for the generalized potentials of the substance which are conjugate to the nonconserved variables such as stresses, heat fluxes, diffusion fluxes, and so on. The results for a couple of special cases are presented without proof.