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In this paper we propose a novel way to design nonparaunitary and paraunitary filter banks so that each individual filter has linear phase. M channel filter banks, which have perfect reconstruction (PR) and linear phase (LP) properties, have been well studied and some design methods were reported. Since almost these methods are based on lattice structures whose sections consist of an orthogonal matrix, the design requires nonlinear programming techniques. Here, we consider a design method which requires only to solve linear equations iteratively. In our proposed method, we minimize the least square error of PR constraints so as to get around using nonlinear programming. We first observe the minimization problem of a quadratic function with two variables. Next, we apply it to the design of nonparaunitary filter banks. Then, we show that this method is applicable to the paraunitary filter banks design with some modification. Several design examples are given to validate our proposed methods.