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We propose a new method of constructing linear phase perfect reconstruction (LPPR) cosine modulated filter banks (CMFB) in the Schuller-Smith framework which is a matrix framework for designing modulated filter banks [Gerald Schuller et al., Aug. 1996]. The design invokes nilpotent matrix formalism which originates from the Schuller-Smith framework. The design uses cosine modulation only and no sine modulation is necessary. The filter bank has an M-band structure in contrast to the conventional 2M-band structures [(X. Q. Gao et al., Apr. 1996) (Yuen-Pei Lin et al., Nov. 1995)] that use both cosine and sine modulations. The design uses discrete cosine transform type-6 (DCT-6).