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Convolutional neural network (CNN) has become the mainstream method in the field of image recognition for its excellent ability to feature extraction. Most of the CNNs increase the classification accuracy for the rotational objects by imposing the network with rotation invariance or equivariance property, which causes the loss of the targets orientation information. This paper attempts to achieve objects recognition and angle or orientation estimation simultaneously without additional network training. To this end, we propose the matching criterion and the kernel-mapping convolutional neural network (KM-CNN). It has been shown that when the kernel satisfies the matching criterion, the output remains the same. Based on this study, we apply rotation transformation to the KM-CNN. Besides, the KM-CNN with the rotation by shifting pixel method and octagonal convolutional kernels can solve the mismatching problem caused by the rotations. The KM-CNN with the kernel sharing central weights gives the near state-of-art results in target recognition and angle estimation on benchmark datasets MNIST, GTSRB and Caltech-256.