This paper presents a new curve reconstruction method based on orthogonal neural network. The orthogonal neural network' s structure is the same as that of the three layered feedforward neural network. The difference is that the processing function of hidden unit of the orthogonal neural network is Tchebycheff orthogonal function instead of sigmoidial function and the calculation of Tchebycheff function is simpler than that of sigmoidial function. The new method uses less samples and reconstructs higher precision smooth curves than previous methods. By adopting a non-iterative Givens learning algorithm

the new network learning algorithm learns fast and can avoid false local minima and the initialization of weights and other parameters. Experiments show that the reconstructed curve using the orthogonal neural network method has high precision not only at learning sample points but also at the non-learning sample points.