Chapman–Enskog expansion is the orthodox approach to derive continuum flow models from Boltzmann’s kinetic equation for dilute gases. Beyond the Navier–Stokes–Fourier order these models, known as Burnett hydrodynamic-regime equations, violate a number of fundamental mechanical and thermodynamic principles in their original forms. This has generated a widely investigated problem in the kinetic theory of gases. In this short article, we derive a Burnett hydrodynamic-regime continuum model that is systematically consistent with all known mechanical and thermodynamic principles without using any series expansion. A close comparison with the conventional Burnett hydrodynamic set of equations is made and the linear stabilities around an equilibrium point under small perturbations are presented.