The effect of the fourth-order truncation error produced by discretizing the convection term was studied on nonlinear characteristics of the solution for the instability of laminar flow and for fully developed turbulent flow. (1) Bifurcation was calculated by the third-order upwind difference method for the Kuramoto-Sivashinsky equation representing the instability of laminar flow. The fourth-order truncation error, however, affected the bifurcation characteristics, and error was introduced for the fourth-mode solution by the Kawamura scheme. (2) Energy spectrum calculated by the third-order upwind difference method for fully developed homogeneous turbulent flow in two dimensions decayed rapidly in a high wave number region in effect of the fourth-order truncation error.