We present a new application of the well-known Hanle effect: the determination of predissociation lifetimes of nonradiating states. A magnetic field depolarizes the angular distribution of the fragments; the degree of depolarization at a fixed field depends on the lifetime of the predissociating state. A semiclassical model is presented to derive lifetimes of predissociative diatomic molecules from the measured angular distributions. This application can be used for lifetime determination of a new class of excited states, predissociative states, in this study represented by the e1Pu (v=0) Rydberg state of N2.