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Quickprop is one of the most popular fast learning algorithms in training feed-forward neural networks. Its learning rate is fast; however, it is still limited by the gradient of the backpropagation algorithm and it is easily trapped into a local minimum. Proposed is a new fast learning algorithm to overcome these two drawbacks. The performance investigation in different learning problems (applications) shows that the new algorithm always converges with a faster learning rate compared with Quickprop and other fast learning algorithms. The improvement in global convergence capability is especially large, which increased from 4 to 100% in one learning problem.