Finding correspondences between two 3D shapes is common both in computer vision and computer graphics. In this paper, we propose a general framework that shows how to build correspondences by utilizing the isometric property. We show that the problem of finding such correspondences can be reduced to the problem of spectral assignment, which can be solved by finding the principal eigenvector of the pairwise correspondence matrix. The proposed framework consists of four main steps. First, it obtains initial candidate pairs by performing a preliminary matching using local shape features. Second, it constructs a pairwise correspondence matrix using geodesic distance and these initial pairs. Next, the principal eigenvector of the matrix is computed. Finally, the final correspondence is obtained from the maximal elements of the principal eigenvector. In our experiments, we show that the proposed method is robust under a variety of poses. Furthermore, our results show a great improvement over the best related method in the literature.