We are concerned with the behaviour of a two-dimensional jet that issues from a planar orifice, with a ‘top-hat’ profile. At the orifice the steady flow is modulated by a time-harmonic fluctuation. A suitably defined Reynolds number is assumed to be large throughout. At large streamwise distances from the orifice, the time-averaged flow yields the classical, Bickley, jet with a suitable virtual origin. This decays algebraically whilst, by contrast, the unsteady component decays exponentially with streamwise distance. An asymptotic theory confirms the exponential decay and provides a good agreement with the numerical solution.