This article offers a new object recognition approach that gives high quality using synthetic aperture radar images. The approach includes image preprocessing, clustering and recognition stages. At the image preprocessing stage, we compute the mass centre of object images for better image matching. A conjugation index of a recognition vector is used as a distance function at clustering and recognition stages. We suggest a construction of the so-called support subspaces, which provide high recognition quality with a significant dimension reduction. The results of the experiments demonstrate that the proposed method provides higher recognition quality (97.8%) than such methods as support vector machine (95.9%), deep learning based on multilayer auto-encoder (96.6%) and adaptive boosting (96.1%). The proposed method is stable for objects processed from different angles.