A new formulation of the classical Navier-Stokes equations is presented, which overcomes the equations' main disadvantage: being a mixed parabolic-hyperbolic system. The new model is achieved by adopting the compressible codeformational time derivative in the stress-strain constitutive relation, resulting in a consistency with the principle of material frame indifference. The main advantage of the new formulation is that the resulting system of equations is purely hyperbolic. The proposed formulation is used to model the benchmark problem of the shock/boundary layer/expansion fan interaction with an apparent degree of success.