Progress in the generation of extremely short pulses of electromagnetic radiation makes the question on the properties of the limiting form of their shortening — unipolar pulses with a significant zero-frequency component of the spectrum, that is, the electric area of the pulse, relevant. Recently, it has been established that it is the electric area that determines the effectiveness of the impact of extremely short pulses on micro-objects. At the same time, unipolar pulses have a number of unusual properties, which makes some researchers doubt the possibility of their existence and propagation. Here we show that a uniformly moving relativistic electric charge creates a short unipolar pulse of the electromagnetic field. This confirms the reality of unipolar electromagnetic pulses, which are promising for applications of extremely short pulses.