The present authors pointed out in the previous paper [1] that the implicit SMAC scheme is quite efficient and non-staggered grid arrangement can decrease the computational effort and save the storage memory which is very important to the direct numerical simulation (DNS) of complicated 3-D flow fields. But using non-staggered grid arrangement, the pressure field oscillation (PFO) ordinarily occurs and also, the pressure on the solid walls including sharp corners need to be prescribed directly as the pressure boundary conditions. In this paper, a new interpolation method, which is a modification to Cheng and Armfield's interpolation formulation, is presented in order to completely prevent PFO from occurring. Moreover, a more accurate specification method of wall pressures and special treatment of pressures at sharp corners are proposed. To test the new methods proposed, the DNS of flow past a square cylinder and flows over backward-facing steps, which are typical of the how fields with sharp corners, is made using the implicit SMAC scheme combined with these methods. The calculated results are compared with the previous experimental and numerical data and show good agreement with them.