Template matching is one of the fundamental techniques for signal and image processing. It has many applications such as detection, recognition, registration, retrieval, etc. One of the drawbacks of the template matching is the high computational complexity. In this paper, we focus on the twodimensional image template matching with fixed aspect ratio and propose a method for speeding up the calculation. In the proposed method, a template is approximated by a polynomial in advance. Given an input image, the normalized cross correlations of the template and the regions of the input image are calculated efficiently with the polynomial. Experimental results using various sizes of images show the effectiveness of the proposed method.