In this work, we present a novel scheme for accurate affine transformation estimation that enables locating large amount of point matches with high geometric precision and low rate of false matches. We show that this is achievable in low computational demand. Point matching is one of the most fundamental tasks in computer vision. It is being extensively used in popular applications like object detection, object tracking, structure from motion and more. Recent publications have shown that considering the affine transformation model of local regions, is extremely beneficial for the purpose of point matching. Although it is not arguable that considering the full affine transformation is extremely beneficial, the use of it in practice is limited as a result of the computational demand. We propose a region expansion method, based on accurate estimation of the affine transformation, which enables prediction of locations beyond the initial local regions. By reducing the amount of false matches considerably, it reduces the need for computationally demanding post processes.