This paper examines the linear hydrodynamic stability of an inviscid compound jet. We perform the temporal and the spatial analyses in a unified framework in terms of transforms. The two analyses agree in the limit of large jet velocity. The dispersion equation is explicit in the growth rate, affording an analytical solution. In the temporal analysis, there are two growing modes, stretching and squeezing. Thin film asymptotic expressions provide insight into the instability mechanism. The spatial analysis shows that the compound jet is absolutely unstable for small jet velocities and admits a convectively growing instability for larger velocities. We study the effect of the system parameters on the temporal growth rate and that of the jet velocity on the spatial growth rate. Predictions of both the temporal and the spatial theories compare well with experiment.