Abstract: The basic theory of independent component analysis (ICA) and the FastICA algorithm are briefly described. Conventional FastICA algorithm has only a second-order convergence rate, which has to be improved to reduce the iteration steps and running time. An improved ICA algorithm is therefore proposed, i.e., the Newton's iteration method with a fifth-order convergence. It is actually a modified Newton's iteration method to enable the improved FastICA algorithm to have fifth-order convergence rate. The simulation results of separating an image signal from others showed that although the algorithm thus improved has the same separating effect as conventional FastICA algorithm, it can greatly reduce the iteration steps and running time further than FastICA, thus increasing the convergence rate and improving the operation efficiency.