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In this study, a nonlinear analysis method called improved information entropy (IIE) is proposed on the basis of constructing a special probability mass function for the normalized analysis of Shannon entropy for a time series. The definition is directly applied to several typical time series, and the characteristic of IIE is analyzed. This method can distinguish different kinds of signals and reflects the complexity of one-dimensional time series of high sensitivity to the changes in signal. Thus, the method is applied to the fault diagnosis of a rolling bearing. Experimental results show that the method can effectively extract the sensitive characteristics of the bearing running state and has fast operation time and minimal parameter requirements.