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In many filter-design problems, additional constraints are often imposed on the optimal filter in the sense of, say, minimal Chebyshev error norm. Based on the characteristic properties of the optimal filter for the Chebyshev design with frequency equation constraints, a modified Remez (MRemez) algorithm is proposed in this paper. The central problem of this paper is the constrained Chebyshev design of finite-impulse response filters with equation and inequality constraints in the frequency domain. By converting the problem into a series of Chebyshev design problems with equation constraints, an iterative MRemez algorithm which uses the MRemez algorithm as the computational core of the iteration is proposed, and the convergence of the algorithm is obtained. Design examples demonstrate the effectiveness and the fast convergence of the MRemez algorithm and the iterative MRemez algorithm.