The essential purpose of this paper is to obtain the fixed point of different functions by using a modern repetitive method. We incorporate concepts suggested in the Bisection method and the Moth-Flame Optimization algorithm. This algorithm is more impressive for finding fixed point functions. We also implement this method for four functions and finally compare the current method with other methods such as ALO, MVO, SSA, SCA algorithms. the proposed method shows a decent functionality than the other four methods.