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In this paper a new shortest path routing algorithm is presented. This algorithm integrates a fast searching strategy into the hysteretic transiently chaotic neural network model which has higher ability of searching optimal solution. By eliminating the components of the eigenvectors with eminent negative eigenvalues of the weight matrix, this proposed method can avoid oscillation and offer a considerable acceleration of converging to the optimal solution when being used to solve the shortest path problems. The numerical simulation results show that the proposed method can quickly find the global optimization solution of the shortest problems.