Abstract: By making use of n-width in approximation theory and Bernstain's inequality, a quasi-optimal upper error bound for two-stage H∞ identification algorithms of robust identification is established in this paper, which is an explict function of general window coefficients. The function is convex with respect to window coefficients. It not only can be used for computation of upper error bounds corresponding to any concrete window coefficients, but also sup- plies a feasible way for choosing window coefficients of two-stage H∞ identification algorithms with optimization techniques.