Motion estimation (ME) is a key operation for video compression. In fact, it contributes heavily to the compression efficiency by removing temporal redundancies. This process is the most critical part in a video encoder and can consume itself more than 50% of coding complexity or computational coding time. To reduce the computational time, many fast ME algorithms were proposed and implemented. The present paper proposes a fast ME algorithm that improves the basic Test Zone Search (TZS) ME algorithm which is considered to be one of the fastest ME algorithms and was implemented in HEVC reference software HM8.0. Experimental results show an improvement that can reach 8% up to 49% compared to the basic TZSearch.