In this article, the new method that solves Initial Value Problems IVPs is presented, where we derived our new method by using the Contra Harmonic CH mean instead of the classic arithmetic mean, more than the Forward Backward FB) technique to calculate both sides of the predictor (Forward) part and corrector (Backward) part of our semi-implicit method. The method was applied to a solved example with a different step size, and the results with the exact and the classical old method were compared with the old method.