The correlation between cluster decomposition and the structure of pulsed supersonic jets of argon clusters is analyzed. The longitudinal and transverse space structures of short supersonic pulses (≈0.5 ms) of argon clusters have been studied far from the skimmer, by a movable mass spectrometer and near the skimmer, by an electron impact ionizer, depending on the stagnation pressure. It has been found that the pulses consist of two distinct fractions of clusters, light and heavy, which are also differently localized in space. The heavy fraction is located inside the pulses and the light fraction is mainly found in the outlying area of the pulses. It has been shown that neutral clusters reveal instability for a long period of time (approximately 0.6 ms) after condensation. This instability results in additional divergence of the cluster beam. Therefore, the change of the cluster beam cross section as a function of the pressure correlates with the corresponding change in the cluster instability.