The reassignment technique is used to increase localization for signal components in the time-frequency representation. The technique gives perfect localization for infinite linear chirp-signals, impulses and constant frequency signals but not for short non-stationary signals. In this paper, a scaled reassignment is proposed, based on the spectrogram using a Gaussian window. The resulting reassignment gives perfect localization for a Gaussian function when the window length matches the function length. Based on the scaled reassignment, an algorithm that estimates the Gaussian function length is also proposed.