  In the present work, we give a numerical solution of the radial Schr\"odinger
equation for new four-parameter radial non-conventional potential, which was
introduced by Alhaidari. In our calculations, we applied the asymptotic
iteration method (AIM) to calculate the eigenvalues of the potential for
arbitrary parameters and any l state. It is found that this method gives highly
accurate results that compares favorably with other. Moreover, some new results
were presented in this paper.
