Abstract: In this paper, an optimized training scheme of neural network for associative memory is proposed. We show that the basins of attraction for samples attractors can be controlled in some extent by a pitfall depth parameter, therefore, the fault-tolerance of network can be made as good as possible. Numerical simulations show that with this scheme, the capacity of network can reach α＜1 (α= M/N, here N is the number of neurons and M is the number of stored samples) and still with good fault-tolerance. The results are much better than the popular schemes such as outer-product scheme, orthogonalized outer-product scheme, pseudo-inverse matrix scheme and etc.. The problems on symmetry and convergence of trained networks are discussed too.