An efficient iterative Lagrange multiplier approach is developed in this paper to design cosinemodulated FIR filter banks with perfect reconstruction.The objective function is formulated as a quadratic function of the prototype filter coefficients whose minimum point can be obtained using the Lagrange multiplier approach in each step. This approach has high design efficiency and is not sensitive to changes in the initial prototype filter coefficients. A design example is presented to demonstrate the effectiveness of the new method.