A procedure is developed to construct a time-limited pulse for its use in the short-range impulse radio communications. The even-numbered shifts of the pulse constitute a train of overlapping pulses. The pulses are intentionally made orthogonal to the second derivative of one another. This orthogonality makes it possible to detect the received pulses, which are assumed to be the second derivative of the transmitted pulses, by means of correlation with the original pulses. An example pulse is presented that complies with the FCC regulation for indoor ultra-wide bandwidth radio communications.