This paper proposes a novel technique for performing fast block matching for motion estimation which is optimal, meaning it yields the same results as a full-search investigation. The proposed technique derives from an approach previously proposed (Tombari et al., 2006) for template matching and it is based on the deployment of a succession of lower bounding functions of the matching metric. Hence, an algorithm is outlined which efficiently exploits these bounding functions in order to rapidly determine non-matching block candidates, thus reducing the overall computational burden. Experimental results show that, compared to the brute-force approach, the proposed technique allows for notable reductions in terms of number of operations and computation times.