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Katabatic flows are notoriously difficult to model for a variety of reasons. Notably, the assumptions underpinning Monin-Obukhov similarity theory (MOST) are inherently violated by the sloping terrain, causing the traditional flux-gradient relations used in numerical weather prediction models to break down for katabatic flows. Focusing on turbulent momentum transport, we show significant flux divergence, further violating MOST assumptions, and that the traditional parameterizations fail even with local scaling for katabatic flow. In response, we propose a modified local-MOST stability-correction function, informed by near-surface turbulence observations collected over two mountainous slopes with inclination angles () of and . The proposed relation includes directly, making data from both slopes collapse with unprecedented agreement. RMSE values for estimating the flux from the proposed and Businger (1971) relations show significant improvement. These results can be used immediately in prescribing the wall-model and turbulence closures in simulations of katabatic flows.