Point pattern matching (PPM) is an important topic in computer vision and pattern recog-nition . It can be widely used in many areas such as image registration, object recognition, motion de-tection, target tracking, autonomous navigation, and pose estimation. This paper discusses the in-complete matching problem of two point sets under Euclidean transformation. According to geometric reasoning, some definitions for matching clique, support point pair, support index set, and support in-dex matrix, etc. are given. Based on the properties and theorems of them, a novel reasoning algo-rithm is presented, which searches for the optimal solution from top to bottom and could find out as many consistent corresponding point pairs as possible. Theoretical analysis and experimental results show that the new algorithm is very effective, and could be, under some conditions, applied to the PPM problem under other kind of transformations. Point pattern matching (PPM) is an important topic in computer vision and pattern recog-nition. It can be widely used in many areas such as image registration, object recognition, motion de-tection, target tracking, autonomous navigation, and pose estimation. According to geometric reasoning, some definitions for matching clique, support point pair, support index set, and support in-dex matrix, etc. are given. Based on the properties and theorems of them, a novel reasoning algo-rithm is presented, which searches for the optimal solution from top to bottom and could find out as many consistent corresponding point pairs as possible. Theoretical analysis and experimental results show that the new algorithm is very effective, and could be, under some conditions, applied to the PPM problem under other kind of transformations.