The Stretched-FrOnt-Leg (SFOL) pulse is a high-accuracy distance measuring equipment (DME) pulse developed to support alternative positioning and navigation for aircraft during global navigation satellite system outages. To facilitate the use of the SFOL pulse, it is best to use legacy DMEs that are already deployed to transmit the SFOL pulse, rather than the current Gaussian pulse, through software changes only. When attempting to transmit the SFOL pulse in legacy DMEs, the greatest challenge is the pulse shape distortion caused by the pulse-shaping circuits and power amplifiers in the transmission unit such that the original SFOL pulse shape is no longer preserved. This letter proposes an inverse-learning-based DME digital predistortion method and presents successfully transmitted SFOL pulses from a testbed based on a commercial legacy DME that was designed to transmit Gaussian pulses.