Proposes an effective technique for searching for critical points, which are points at which the velocity vector is zero. The previous method, using tetrahedral-cell subdivision, often generates multiple critical points in a hexahedral cell, and this causes several defects in flow visualization. First, we propose a new criterion for differences between interpolation functions, and investigate the reasons for the generation of multiple critical points in a hexahedral cell. Next, to prevent the generation of multiple critical points, we propose an improved method using both tetrahedral-cell subdivision and a trilinear interpolation function. Our method finds critical points by using a linear interpolation function, and, when multiple critical points are found in a hexahedral cell, a numerical integration scheme (Newton's method) is applied and a more precise position is calculated. We apply our approach to several sets of velocity data and evaluate it in several ways.