The Rapid Burster (MXB 1730-335) is a unique X-ray source which produces rapidly repetitive X-ray bursts. Each rapid burst shows a characteristic structure in its decay part comprising successive peaks. The authors have discovered that the structure of each individual burst shows a nearly identical profile except for the timescale, which differs largely from burst to burst; the profile of the decay is timescale invariant. This invariance holds over a wide range of timescales to at least a factor of 30.