This paper presents a hierarchical method for finding correspondences in non-rigid shapes. We propose a new representation for 3D meshes: the decomposition tree. This structure characterizes the recursive decomposition process of a mesh into regions of interest and key points. The internal nodes contain regions of interest (which may be recursively decomposed) and the leaf nodes contain the key points to be matched. We also propose a hierarchical matching algorithm that performs in a level-wise manner. The matching process is guided by the similarity between regions in high levels of the tree, until reaching the key points stored in the leaves. This allows us to reduce the search space of correspondences, making also the matching process efficient. We evaluate the effectiveness of our approach using the SHREC'2010 robust correspondence benchmark. In addition, we show that our results outperform the state of the art. © 2013 IEEE.