The well-know pseudo-spectral second-order splitting method has been the work-horse algorithm for solving the time-dependent Schrodinger equation for decades. However, it has been only ~30 years that one learns how to generalize this algorithm to fourth and higher orders. During that period, one also learned about the crucial distinction between solving time-reversible and time-irreversible quantum evolution equations. In this work, I show that there is only one class of fourth-order, forward time step algorithm that can solve both time-reversible and time-irreversible equations with equal efficiency. Other higher order algorithms based on multi-product expansion and complex coefficient will also be mentioned.