This paper introduces a pruning algorithm with tridiagonal symmetry constraints for feedforward neural network design. The algorithm uses a reflection transform applied to the input--hidden weight matrix in order to reduce it to its tridiagonal form. The designed FANN structures obtained by applying the proposed algorithm are compact and symmetrical. Therefore, they are well suited for efficient hardware and software implementations. Moreover, the number of the FANN parameters is reduced without a significant loss in performance. We illustrate the complexity and performance of the proposed algorithm by applying it as a solution to a nonlinear regression problem. We also compare the results of our proposed algorithm with those of the Optimal Brain Damage algorithm. EDICS: SP 6.1.5 This work was supported by the Natural Sciences and Engineering Research Council of Canada under contract #06P--0187668. 1 Introduction Feedforward neural network (FANN) design has lately attracted...