This paper proposes a novel algorithm aimed at speeding-up template matching based on the L_p norm. The algorithm is exhaustive, i.e. it yields the same results as a Full Search (FS) template matching process, and is based on the deployment of tight lower bounds that can be derived by using together the triangular inequality and partial evaluations of the L_p norm. In order to deploy this, template and image subwindows are properly partitioned. The experimental results prove that the proposed algorithm allows speeding-up the FS process and also (when applied to the L_2 norm) the exhaustive approach based on the Fast Fourier Transform.