The objective of the paper is to develop new block matching Motion Estimation (ME) algorithm using hybrid search patterns along the direction of best match. The search efficiency for sequences with fast motions and high resolutions is improved by proposing New Cross Diagonal-Hexagon Search (NCDHS) algorithm which involves a novel multi half-hexagon grid global search pattern and a cross diagonal-hexagon local search pattern. The new search pattern enables the proposed algorithm to perform better search using 9.068 search points on an average, to obtain optimal motion vector with slight improvement in quality. This inturn reduces ME Time upto 50.11%, 47.12%, 32.99% and 43.28% on average when compared to the existing Diamond Search (DS), Hexagon Search (HS), New Cross Hexagon Search (NHEXS) and Enhanced Diamond Search (EDS) algorithms respectively. The novelty of the algorithm is further achieved by applying the algorithm proposed for live streaming application. The NCDHS algorithm is run on two MATLAB sessions on the same computer by establishing the connection using Transmission Control Protocol (TCP) /Internet Protocol (IP) network. The ME Time obtained is 14.5986 seconds for a block size 16x16, is less when compared to existing algorithms and that makes the NCDHS algorithm suitable for real time streaming application.