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We report an experimental and theoretical investigation of the four-wave mixing (FWM) process between a coherent signal light and an incoherent pump light in a highly nonlinear fiber. In the experiment, two main phenomena are observed: 1) the peak power of the spectrum of the coherent signal light decreases along the fiber rather than be amplified; 2) the spectrum of the coherent signal is broadened. A theory of the FWM process between incoherent pump and coherent signal is proposed by considering the incoherence of the pump which has amplitude and phase fluctuations. The theoretical results agree with the experimental results.