The paper proposes a technique aimed at reducing the number of calculations required to carry out an exhaustive template matching process based on the normalized cross correlation (NCC). The technique deploys an effective sufficient condition, relying on the recently introduced concept of bounded partial correlation that allows rapid elimination of the points that cannot provide a better cross-correlation score with respect to the current best candidate. In this paper we devise a novel sufficient condition based on the Cauchy-Schwarz inequality and compare the experimental results with those attained using the standard NCC-based template matching algorithm and the already known sufficient condition based on the Jensen inequality.