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In multirate digital signal processing, cosine-modulated filter banks (CMFB) satisfying perfect reconstruction (PR) or near-perfect reconstruction (NPR) property are of great interest owing to their extensive applications in data compression, feature detection and extraction and signal transmultiplexing. And the key to PR CMFB design is to design a PR prototype filter (PF). However, designing optimal PR and NPR PF is essentially a constrained non-linear programming. It is generally modelled as a non-convex quadratically constrained quadratic optimisation problem. So far, this kind of optimisation is still a very difficult class of optimisation and no practical but few metaheuristic algorithm is availabe for finding its global optimal solution. The study proposed a two-stage method for designing PR PF. In the first stage, a metaheuristic algorithm based on variable neighbourhood search is proposed for designing lower-ordered PR PF, that is the corresponding PR CMFB has less channels. Then a least-mean-square error approach is introduced to increase the length of the designed lower-ordered PF with the PR property unchanged. Design examples are given to illustrate the proposed algorithm outperforms the existing one in reconstruction error and stopband attenuation.