A new chaotic map was created to improve on the limitations of the logistic chaotic map. By analyzing the behavior of both maps, it was found that the new map is more random and has better performance evaluation indices. The researchers defined a new measure, the bifurcation iteration time, to assess the chaotic system's behavior. Simulation results showed that the new map is not only ergodic but also outperforms the traditional logistic map in generating chaotic sequences.