We present a method for the retrieval of the imaginary part of refractive index of desert dust aerosol at near UV wavelengths. The method uses observations of radiances at 331 and 360 nm by the Total Ozone Mapping Spectrometer, and aerosol optical depth measurements by the Aerosol Robotic Network. The derived values of imaginary part of refractive index of Saharan dust aerosol at 360 nm are significantly lower than previously reported values. The average retrieved values vary between 0.0054 and 0.0066 for different geographical locations. The results reported in this work are in good agreement with the results of several recent investigations.