We propose a new physiologically-based outflow boundary condition for hemodynamics under general transient regimes. This is in contrast to previous studies that impose restrictions of temporal periodicity. The new condition is analyzed and its numerical implementation is discussed in detail. We show that existing impedance boundary conditions can be viewed as numerical approximations of the new condition. Our study provides a partial justification for using some of these existing conditions beyond the periodic problems for which they were designed. Moreover, the new condition has better stability properties. The theoretical results are illustrated by numerical experiments pertaining to cerebral blood flow.