A point vortex located above and convected parallel to a wall is an important model of the process by which a boundary layer becomes unstable due to external disturbances. Often it has been assumed that the boundary layer due to the passage of the vortex is inherentlyunsteady. Here we show that for a vortex convected by a uniform shear flow, there is asteadysolution when the speed of the vortexcvis sufficiently fast. The existence of the steady solution is demonstrated analytically in the limit of large vortex velocity (cv→∞) and numerically at more moderate speeds. This solution may provide a useful base state about which to investigate the stability of a boundary layer induced by external disturbances. ©1995 American Institute of Physics.