Abstract: A new implicit factored difference scheme for solving compressible Navier-Stokes equations on the base of the single step scheme developed before is described in this paper. For the inviscid portion of the Navier-stokes equations the flux vectors are split according to the sign of the eigenvalues of the Jacobian matrices using the property that the nonlinear flux vectors are homogeneous functions of degree one. For the viscous portion correction with operator the addition is used for improving convergence rate. Obtained difference scheme is used to solve Couette flow.