  We perform time-resolved spectroscopy of all the type I bursts from the Rapid
Burster (MXB 1730-335) detected with the Rossi X-ray Timing Explorer. Type I
bursts are detected at high accretion rates, up to \sim 45% of the Eddington
luminosity. We find evidence that bursts lacking the canonical cooling in their
time-resolved spectra are, none the less, thermonuclear in nature. The type I
bursting rate keeps increasing with the persistent luminosity, well above the
threshold at which it is known to abruptly drop in other bursting low-mass
X-ray binaries. The only other known source in which the bursting rate keeps
increasing over such a large range of mass accretion rates is the 11 Hz pulsar
IGR J17480$-$2446. This may indicate a similarly slow spin for the neutron star
in the Rapid Burster.
