In this paper, we propose a novel corner transformation-based algorithm CTCBMQ (corner transformation-based algorithm for continuous border monitoring query) for Continuous Border Monitoring Query processing (CBMQ) over moving object streams, CTCBMQ transform the CBMQ processing problems into the spatial join processing problems. Based on the transformation, CTCBMQ finds stream-query pairs which satisfy intersecting relationship. Another attractive contribution of our work is utilizing the locality characteristic of moving objects. To take advantage of this characteristic, we cache the search result via a special design. When a hit occurs, we reuse the cache result, avoiding re-evaluate the queries once again. Experimental results show that CTCBMQ significantly outperforms existing approaches in term of both storage cost and search time.