To address the computing instantaneous frequency of the product function (PF) in local mean decomposition (LMD), a new instantaneous frequency of a signal computing method was introduced. This method is piece-wise wave based. Firstly, a signal was separated to a number of full waves. Then, the instantaneous phase of each full wave was defined by a set of monotonic increasing arcsine functions. Therefore, the instantaneous frequency of a signal was obtained. Theoretically, the instantanoues frequency obtained in this method was positive, stable and could guarantee the characteristic information of signal integrity. This method was applied to compute the instantaneous frequency of simulated signals and actual gear fault vibration signals, and the results were compared with those obtained in other methods. It has been shown that this method is quite suitable for extracting the instantaneous frequency of a signal.