A bundle of many parallel fibers, with stochastically distributed thresholds for individual fibers, is loaded until complete failure. Equal load sharing is assumed. During the breakdown process, bursts of several fibers breaking simultaneously at a given load occur. We determine the expected number of such bursts before complete failure, as well as the frequency of bursts in which Δ fibers break simultaneously. This distribution follows asymptotically a universal power-law Δ−5/2, for any statistical distribution of the individual fiber strengths.