Motion Estimation (ME) is a core part of most Video compression systems since it affects directly the output video quality and the encoding time. The most basic method of ME, Full Search (FS) gives the highest visual quality but also has the problem of significant computational load. To solve this problem, many fast algorithm has been proposed. Among them, MVFAST and PMVFAST show impressive results in video quality and the computational load by using the correlation between motion vectors of adjacent blocks. In particular, PMVFAST reduces search points dramatically and also gives very high video quality by using the median predictor. In this paper, we propose a new algorithm that uses the redefined median predictor which reduces the number of search points and yields a high visual quality by reducing the number of thresholds and early termination conditions.