The instability of a high‐speed liquid jet with a velocity which has a transient rise followed by a linear decay with time is studied experimentally and theoretically. The jet is produced experimentally by subjecting a liquid reservoir to a shock‐wave pressure. Using a shadowgraph technique, in an interval of thirty microseconds four successive quarter‐microsecond exposures were taken using jets of water and ethanol in external atmospheres of air and helium. It is found theoretically that a velocity discontinuity is advanced through the jet at a velocity which is the mean of the instantaneous particle velocities immediately in front of and behind the discontinuity. The discontinuity consists of a thin disk of liquid normal to the jet axis. Nodules previously observed on high‐speed liquid jets [J. Appl. Phys.25, 569 (1954)] can be explained by this mechanism.