Side jet formation in variable-density round jets is investigated by means of direct numerical simulation (DNS) and linear stability analysis. From DNS, it is observed that a light jet with density ratio S = ρ0/ ρj = 4 supports sustained side jets which eject fluid from the center of the jet in a star-shaped pattern. These side jets persist over an axial distance of approximately 5 jet diameters before the jet transitions to turbulence, and do not precess around the jet. It is conjectured that this behavior can be explained by a change in the local properties of the secondary instability from convective to absolute in nature. This hypothesis is tested by examining the spatio-temporal development of the wavepacket resulting from a small impulse, taken about a non-diffusing periodic base state corresponding to the saturated primary instability.