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This paper proposes an efficient iterative linearization method for designing a class of cosine modulated filter banks (CMFBs) with linear phase (LP) property satisfying perfect reconstruction (PR). In this paper, the design of the prototype filter is formulated as a quadratic-constrained optimization function of the prototype filter coefficients whose minimum point can be obtained using the Lagrange multiplier approach at each step. The main advantages of this method are simple design procedure and high computational efficiency. A design example is presented to demonstrate the effectiveness of this new method.