A regularization procedure of the Chapman-Enskog expansion is introduced. It extends the hydrodynamical description into higher gradients domains. This was intended but never accomplished satisfactorily by the Burnett equations. The resulting macroscopic system formally has the same form (and complexity) as the Navier-Stokes equations, with the new transport coefficients being wavelength dependent. It reduces in the long-wavelength limit to the Burnett equations. In agreement with experimental evidence, strong shock layers are narrower in comparison with the predictions of the Navier-Stokes theory.