  In this article, we present the analytical solution of the radial
Schr\"{o}dinger equation for the Hulth\'{e}n potential within the framework of
the asymptotic iteration method by using an approximation to the centrifugal
potential for any $l$ states. We obtain the energy eigenvalues and the
corresponding eigenfunctions for different screening parameters. The wave
functions are physical and energy eigenvalues are in good agreement with the
results obtained by other methods for different $\delta $ values. In order to
demonstrate this, the results of the asymptotic iteration method are compared
with the results of the supersymmetry, the numerical integration, the
variational and the shifted 1/N expansion methods.
