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This paper proposes an algorithm to design a two-channel linear phase quadrature mirror filter (QMF) bank. The design problem is presented systematically as an unconstrained optimization that minimizes the weighted sum of error of transfer function of the filter bank at quadrature frequency, stopband energy and the passband error of a prototype filter (PF). A new method is developed for the design of a low pass prototype filter for QMF banks. For solving given optimization problem, Quasi-Newton optimization technique is used. Numerical examples and comparisons with several existing methods are included to show the performances and effectiveness of this method. An application of the proposed method is considered in the area of subband coding of the images.