Local rub-impact is common faults in rotating machinery and results in impact and friction between rotor and stator. The vibration signals due to impact and friction are always non-stationary which includes the rub-impact signal, the background signal and the noise signal. Local wave decomposition (LWD) is based upon the local characteristic time scale of signal and could decompose the complicated signal into a number of intrinsic mode functions (IMFs). However, because the weak rub-impact signal is always submerged in the background and noise signals. The LWD procedure would generate the components redundancy. In order to solve the problem, a novel method combining with independent component analysis (ICA) and LWD is proposed. ICA was introduced into LWD, so that the components are orthogonal to each other and the components redundancy can be removed. In the end, a much better decomposition performances can be obtained. Experimental analysis results show that the proposed method is accurate and efficient.