Euler introduced the famous Euler method in 1728. As the simplest and the most analyzed numerical integration, it has become the stepping-stone of numerical methods for solving Initial value Problems in Ordinary Differential Equations. There has been considerable efforts to improve on Euler method by increasing its order of accuracy. Recently, in , Abraham proposed a new improvement on Euler Method called Modified Improved Modified Euler Method. In this work, we investigate the basic properties of this new method vis-à-vis the older ones. Our analysis show that the method is convergent to order 2 and stable when applied to autonomous Initial Value Problem.