Based　on　a　new　way　to　compute　check　points,　this　paper　presents　a　＇Block　Recursive＇　sequence　alignment　algorithm,　which　can　run　in　a　time　requirement　between　1.5mn　and　3mn　in　general　cases　but　between　1.5mn　and　2mn　for　sequences　with　high　similarities.　Still,　the　algorithm　keeps　a　linear　space　requirement　and　always　guarantees　an　optimal　alignment　result.　Some　experiments　show　that　it　runs　at　least　10%　faster　than　the　Hirschberg　algorithm　if　the　two　compared　sequences　has　a　normalized　edit　distance　less　than　0.25.　©　2008　IEEE.