In regions where strong katabatic winds occur, notably Commonwealth Bay, Antarctica, there is often a sharp boundary between the strong winds and the comparatively calm conditions at sea. The seaward movement of this boundary across a coastal station is accompanied by a sudden onset of strong winds and the landward movement by their sudden cessation. The boundary has all the characteristics of a pressure jump line accompanying a sudden change in depth of the cold air. Further-more, it is to be expected from theoretical considerations that a pressure jump will occur near the coast. A simple theory is developed from which various characteristics of the flow can be predicted, including the intensity of the jump and the deviation of the wind from the lines of greatest slope caused by the Earth's rotation. These predictions agree moderately well with observations.