An efficient and robust iterative solver was proposed to solve the five-diagonal matrix equations that arise from implicit discretization of two-dimensional thermal and fluid flow problems. By regarding the well-known ADI solver and the direct solver as the lowest and the highest levels of matrix decomposition, a systematic investigation was carried out to identify which level of matrix decomposition is then most suitable for the five-point formulation currently in use. Also, the existing block-correction procedure is implemented by deliberately evaluating the residual. In this way, both the high- and low-frequency errors are efficiently reduced so that the new iterative solver provides savings of about an order of magnitude in the computational cost. As the grid size increases, the new solver presented here turns out to be more powerful and more robust than other iterative solvers previously available.