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We studied noise effect of neuron on its spiking timing in a leaky integrate-and-fire (LIF) neuron with both input noise and fluctuant threshold. By solving the first-passage problem with a new method which can treat LIF systems with both input and threshold noises, we have found a new beneficial effect of noise, in which neuron threshold noise do not disperse neuron inter-spike interval (ISI) distribution, but concentrate ISI distribution dispersed by input noise. The nonlinear mechanism and condition of this positive noise effect have been demonstrated in this paper.