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We propose a simplified version of lattice factorization for linear-phase perfect reconstruction filter bank (LPPRFB) derived by T.D. Tran et al. (see IEEE Trans. Signal Processing. vol.48, no.1, p.133-47, Jan. 2000). The proposed new lattice structure spans the same class of LPPRFB, while substantially reducing free parameters in nonlinear optimization and saving computation cost in hardware implementation. To further address the importance of our proposed structure, we generalize our factorization to multidimensional LPPRFB (MD-LPPRFB), and show its effectiveness.