In this paper, we present a new eight-step singularly P-stable method with vanished
phase-lag and its derivatives up to fifth order for the numerical integration of the one-dimensional
radial time independent Schrodinger equation. Numerical stability and phase properties of the
new methods are analyzed and the periodicity region of the method has been plotted. Finally
we compare the new method to the corresponding classical ones and other known methods from
the literature to demonstrate the high efficiency of our new method.