N-body simulation is the necessary tool to investigate the evolution of star clusters. It is important to develop a time integration method which guarantees the appropriate accuracy and calculation cost.

Here we present a new simple method for long term simulation of stars around a massive black hole in stellar systems. Usually the time integration orbits of stars revolving a massive black hole requires much simulation time. We introduce a time transformation which is a kind of ”inverse KS regularization” of time. Using our method, the integration of the long term evolution near a black hole (BH) becomes easier, especially applied to relatively large star clusters and the Galactic Center.