In the context of motion estimation (ME) for video coding, the rate-constrained successive elimination algorithm (RC-SEA) safely eliminates candidate motion vectors while preserving the optimal candidate chosen by the block matching algorithm (BMA). This paper describes a technique for reusing ME information from rectangular to square prediction units in order to reduce the search area without altering the optimal candidate chosen by the BMA. Our experiments show that, on average, when this optimization is combined with the RCSEA in the HEVC HM encoder reference software, the number of sum of the absolute differences (SAD) operations drops by 94.9%, resulting in a speedup of 6.13x in full search mode. Although identical coding decisions cannot be guaranteed when multiple optimal solutions exist, the average impact on BD-PSNR is 0.0002 dB.