A new method to increase the sensitivity of the 1D transient NOE experiment for molecules in the positive NOE regime is presented. This method, the reverse NOE, simply replaces the conventional relaxation delay between scans. Transient positive NOE enhancements from all other spins are used to accelerate the recovery of the target resonance toward its equilibrium intensity. In favorable cases, the intensity of the target peak at the start of an experiment can actually be increased beyond its equilibrium value. There is also a sensitivity enhancement in the rapid pulsing regime, where recovery is always incomplete. This sensitivity enhancement is illustrated with the one-dimensional double pulsed field gradient spin echo NOE experiment to observe a "fourth-order" NOE. Sensitivity gains of 30% are demonstrated.