A lifetime distribution is forgetful at certain points if it obeys the classical lack-of-memory property at these points. In this paper, a new notion about the memory property of lifetime distributions is introduced in terms of what we call the φ-forgetful property. We prove a theorem for the existence of this property for all lifetime distributions. This theorem is used to characterize lifetime distributions such as the Weibull, Pareto, Gompertz, and extreme value.