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A leing algorithm is presented for the leing of neural networks,in which the leing trajectory is convergence without any over-leing by changing of topological construction of the algorithm near any local minimum points of leing error.Because the topological construction is not convergent for some functions by usual BP method near some local minimum points,there is an over-leing phenomenon.To avoid the over-leing phenomenon, reference-following variables are used to change the topological construction of this algorithm.The theoretical analysis and the simulation results indicate that the proposed method is simple and useful.