Abstract: The directional relation is regarded as one of the indispensable contents in completely spatial relation expresssing. In view of the deficiency of directional relation matrix in uniform directional qualitatively expressing and reasoning for self directional relation of concave region, according to spatial relativization, this research improves and perfects the algebraic direction relations expressing and reasoning qualitively between target object and concave landmark using global external and local internal directions. Firstly, the global external directional relation for reference concave polygon and target object is achieved based on trisection affine transformation matrix. Secondly, the local internal directional relations between concave polygon and target object are presented through concave adaptive segmentation. Thirdly, the qualitive directional reasoning based on vector triangle rule from two concave reference landmarks is realized via integration logical composing operator, as well as single concave reference landmark by difference logical composing operator identically. Last but not least, through experimental instance comparision and analysis, this method was proved to be promising.