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Multibiometrics can provide higher identification accuracy than single biometrics, so it is more suitable for some real-world personal identification applications that need high-standard security. Among various biometrics technologies, palmprint identification has received much attention because of its good performance. Combining the left and right palmprint images to perform multibiometrics is easy to implement and can obtain better results. However, previous studies did not explore this issue in depth. In this paper, we proposed a novel framework to perform multibiometrics by comprehensively combining the left and right palmprint images. This framework integrated three kinds of scores generated from the left and right palmprint images to perform matching score-level fusion. The first two kinds of scores were, respectively, generated from the left and right palmprint images and can be obtained by any palmprint identification method, whereas the third kind of score was obtained using a specialized algorithm proposed in this paper. As the proposed algorithm carefully takes the nature of the left and right palmprint images into account, it can properly exploit the similarity of the left and right palmprints of the same subject. Moreover, the proposed weighted fusion scheme allowed perfect identification performance to be obtained in comparison with previous palmprint identification methods.