Within the framework of the Milburn model of intrinsic decoherence [G. J. Milburn, Phys. Rev. A 44, 5401 (1991)], which is based on an assumption of an existence of the fundamental time step, we study the dynamics of open systems. We show that evolution of an open system governed by the Milburn equation can be significantly modified compared to the standard Schr\"odinger quantum mechanics. This modification is most pronounced when an open system is strongly coupled to its environment.