In this paper, the linearization iterative method in frequency domain for the design of recursive digital filters having a desired spectral density characteristic is proposed. For getting the initial solution, the separat-ion of spectra algorithm is employed. This initial solution affects hardly the rate of convergence of the already existing (steepest descent) algori-thm. However a care has been made to the choice of the initial condition which has consequently lead to a better perfomrance than that obtained using nonoptimal initial solution for the same number of iterations. For the same near optimal initial solution the linearization algorithm has been applied. This algorithm has lead finally to a design procedure by which the filter parameters best approximate the desired specifications with smaller number of iterations. The extensive study of the practical results of the proposed and already existing algorithms has shown that, with the same initial solution the linearization results in a better performance with less computation time.