Abstract: High order FastICA algorithms have the advantages of simple form and fast convergence rate. However, they are sensitive to their initial values affecting convergence effect and even resulting in inconvergence if the initial values are not chosen appropriately. To solve the problem, the FastICA algorithms of the third and fifth order convergence were improved with the steepest descent method. First, the initial values were calculated with the steepest descent method. Then, the optimal solution was calculated with the high order convergence FastICA algorithm. Speech signal separation experiments showed that the improved algorithm can separate mixed signal and overcome the initial value sensitivity problems effectively.