In two-dimensional incompressible flows, a preconditioning technique called Hierarchical Iterative Procedure (HIP) has been implemented on a SUPG finite element formulation. By using the SUPG formulation, one can escape from the LBB constraint hence, achieving an equal order formulation. In this paper, we increased the order of interpolation up to cubic. The conjugate gradient squared (CGS) method is used for the outer iteration, and the HIP for the preconditioning for the incompressible Navier-Stokes equation. The hierarchical elements have been used to achieve a higher order accuracy in fluid flow analyses, but a proper and efficient iterative procedure for higher order finite element formulation has not been available, thus far. The numerical results by the present HIP for the lid driven cavity flow showed the present procedure to be stable, very efficient, and useful in flow analyses, in conjunction with hierarchical elements.