Many motile chemotactic bacteria (for instance, Escherichia coli) inoculated at some point in a semisolid nutrient medium can form circular expanding population waves. The formation of these motile structures is due to chemotaxis. The circular waves originate from an expanding bacterial lawn (a parent population). The regular shape of these waves results from the isotropic distribution of freely diffusible nutrient molecules which are also attractants. In this paper we show that the regular shape of the bacterial population waves can be spontaneously disturbed. As this takes place arc-shaped population waves ('bursts') are formed. It was found that initially the mean length of the cells forming the bursts was greater than that of the parent cell population. But then it decreased resulting in a value characteristic of the parent population.