To solve the initial values impact of the inter-harmonic detection based on high order FastICA, an inter-harmonic detection method based on improved single channel FastICA with relaxation factor is proposed. Firstly, a multi-channel signal observed is formed by cycle-spinning of single channel mixed single, then dimensionality of the multi-channel signal is reduced by principal component analysis. Secondly, by using the relaxation factor which is calculated with the steepest descent method to modify the iterative initial value. Lastly, the symmetry orthogonalization FastICA algorithm is applied to get the frequency of inter-harmonic, and the inter-harmonic amplitude and phase is accurately obtained by using the least squares method. Simulation results show that the algorithm can accurately obtain the inter-harmonic frequency as well as the corresponding harmonic parameters, and also reduce the sensitivity to initial value of the higher order algorithm.