Establishing robust correspondences between two images is important for computer version tasks. However, in the real scene incorrect correspondences are inevitable no matter what kind of correspondence matching algorithms are adopted due to some complex factors, such as illumination, occlusion, and so on. To reduce the number of incorrect correspondences, an algorithm with the same object and same position constraints (SOSPC), is proposed to remove wrong correspondences from the given putative correspondences in this paper. The algorithm is based on the fact that in the given image pairs correct correspondences locate at the same position on the same objects. To select the correspondences on the same objects, an object matching method based on the correspondences selected by GMS is proposed. To select the correspondences on the correct positions, an iterative fundamental matrix estimation method based on clustering is presented. The experimental results have validated the effectiveness of the same object and the same position constraints, and the method achieves the state-of-art performance on five datasets.