An efficient compression algorithm is vital for storage and transmission of video signal. Many video coding standards such as ISO MPEG-1/2 and ITU-T H.261/262/263 apply block motion estimation and compensation algorithms to exploit temporal redundancies where reduction is the key to high performance in video coding. The full search algorithm is a brute force for block motion estimation method used in the standards. It offers the best quality so far but its high computational complexity makes it unsuitable for real-time implementations. This thesis proposes and demonstrates a new scanning order that will minimize the computational complexity of the matching process especially in full search algorithm either with similar or acceptable degradation in quality performance.