The bedform of sediment that is deposited from turbidity currents onto the ocean floor is often found to exhibit long-wavelength variations, with crest lines perpendicular to the flow direction (" sediment waves"). A temporal linear stability analysis, based on the 2D Navier-Stokes equations, reveals the presence of unstable waves in the bottom boundary layer of a turbidity current. Instability arises from the interaction between the current and the sediment bed, via the competing effects of particle deposition and erosion. Due to the velocity and density variations within the current, small undulations of the sediment bed lead to the formation of internal waves. These waves may, under specific flow conditions, amplify the wavy bedform deformation. Unstable sediment waves display long wavelengths and are typically found to slowly travel upstream. Both features are in qualitative agreement with field observations on sediment waves on the backslope of channel levees.