This paper proposes a new fast template matching algorithm that skips comparison between a template and search windows neighboring an already compared dissimilar sub-window. Comparison skipping is executed when a lower bound of distance between the template and a window exceeds a threshold. The lower bound of distance between the template and the window is determined by the triangular inequality in distances: the distance between a subtemplate and a subwindow and that between inter-subtemplates. Experimental results demonstrate that the proposed method is up to five times faster than the conventional fast exhaustive search method (sequential similarity detection algorithm), strictly guaranteeing the same accuracy.