Using　a　new　way　to　compute　check　points,　the　authors　present　the　Block　Recursive　Sequence　Alignment　Algorithm　with　a　linear　space　requirement　between　5(m+n)+Lsmin(m-1,　n-1)+C2and　5(m+n)+Ls(m+n-2)+C2for　the　given　two　sequences　which　length　is　m,　n　apparatively.　The　algorithm　has　a　time　requirement　between　1.5mn　and　3mn　in　general　cases　but　between　1.5mn　and　2mn　for　sequences　with　high　similarities.　Some　experiments　in　aligning　genomes　from　homology　species　have　further　shown　that　it　runs　correctly　and　at　least　10%　faster　than　that　of　the　Hirschberg　Algorithm　if　the　two　compared　sequences　have　a　normalized　edit　distance　less　than　0.25.