This paper introduces a new fast motion estimation based on a maximum matching error constraint that can eliminate an impossible candidate block much earlier than a conventional partial distortion elimination (PDE) scheme. The main contributions of the proposed scheme are that 1) it can reduce the computational cost considerably for the matching error calculation; and 2) the proposed matching ideas can be applied to the conventional PDE algorithms without significant changes. In order to evaluate the proposed scheme, we compare the results of the proposed algorithm with several baseline approaches. The experimental results show that the proposed algorithm can reduce the computations more than 62% for motion estimation at the cost of 0.005 dB quality degradation versus the general PDE algorithm.