ABSTRACT Gravitational waves from precessing binary black holes exhibit new features that are absent in non-precessionary systems. All current waveform models take into account only the modulation of the signal due to precession. In this letter, we find that this effect has its own signature, by gravitational emission of a short and transient signal, or burst. The frequency of the burst is comparable to that of the late stage of the inspiral. We show that under certain conditions, this signal is strong enough to be detected by Advanced LIGO. For third-generation detectors like the Einstein telescope, the calculated signal-to-noise ratio can reach higher values. Measurements of precession would provide valuable insights into the intrinsic structure of black holes, and therefore into astrophysical binary formation mechanisms.