A special experimental setup with a three-electrode discharge gap was used to study the dynamic characteristics of the ultra-high- and super-high-frequency (UHF-SHF) electromagnetic radiation of a high-voltage discharge having the streamer form with reference to the dynamics of individual streamers at the nanosecond time resolution. We performed synchronous detection of the radiation waveforms using a wideband horn antenna, on the one hand, and high-speed photography of the discharge development in the discharge gap using an ICCD camera, on the other hand. It was found that the high-voltage discharge is a source of radiation in the frequency band up to 10 GHz, which is a series of individual ultrawideband (UWB) bursts having durations of less than 1 ns and leading fronts less than 100 ps long and appears when the streamers moving from the discharge anode (thin wire) meet the discharge cathode (plane). By the order of magnitude, the number of radiation bursts corresponds to the number of streamers that reach the electrode, according to the high-speed photography data. The qualitative data confirmed by simple theoretical estimations show that the sources of UWB radiation pulses are individual streamers at the moment of their contact with the electrode, and the radiation of the streamers can be regarded as transition radiation.