A new local search method for the design of linear phase FIR filters with discrete valued coefficients is introduced in this paper. Conventional minimax criterion and normalized peak ripple magnitude (NPRM) are taken as objective functions. The principle is to search along low gradient routes with priority and to direct the search toward steeper sides as improved solutions cease to appear. The characteristics of the objective functions have been explained and used to devise the method. The method is novel in the way it generates the gradient information and makes use of it. At each step, a number of filter coefficients are picked according to the gradient information and perturbed to look for improved solutions. A specific neighborhood definition is proposed and used in perturbing the coefficients. The method has very low computational demand and is suitable for the design of long filters. The results of design examples demonstrate that the performance of the method can compete with those of optimal methods. Along the way, a closed form expression for the "filter gain" that minimizes NPRM is also given. Furthermore, it is shown that a previously proposed local search method unintentionally implements the ideas of this paper in an opposite order. (C) 2002 Elsevier Science B.V. All rights reserved.