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A new discrete cosine transform is developed in such a way that its closeness to the Karhunen–Loeve transform can be established straightforwardly. The transform is characterized by a symmetric matrix and will be referred to as the symmetric cosine transform (SCT). It is shown that a simple window on the data vector makes its covariance matrix more tractable for the SCT. Since the derivation of the SCT is, to some extent, similar to that of the fast KLT proposed by Jain, its advantages over the FKLT are discussed. The new transform is also compared with the conventional DCT proposed by Ahmed et al. The performance of the SCT is better than that of the DCT with respect to computational efficiency, the residual correlation, and the rate-distortion criterion. The SCT is also convenient in hardware implementation as both the forward and reverse operations can be handled by a single apparatus.