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This paper proposes the kernel orthogonal mutual subspace method (KOMSM) for 3D object recognition. KOMSM is a kernel-based method for classifying sets of patterns such as video frames or multiview images. It classifies objects based on the canonical angles between the nonlinear subspaces, which are generated from the image patterns of each object class by kernel PCA. This methodology has been introduced in the kernel mutual subspace method (KMSM). However, KOMSM is different from KMSM in that nonlinear class subspaces are orthogonalized based on the framework proposed by Fukunaga and Koontz before calculating the canonical angles. This orthogonalization provides a powerful feature extraction method for improving the performance of KMSM. The validity of KOMSM is demonstrated through experiments using face images and images from a public database.