Here we give the proof of a general theorem concerning irreversibility that was stated earlier by Misra and Prigogine. In terms of a unitary group describing a deterministic dynamical evolution and a related Markov semigroup describing an associated coarse grained probabilistic evolution, it is shown that the original dynamics are necessarily those of a Kflow. Thus a reversible dynamics which permits such an intertwining to an irreversible description must possess a high degree of instability.