In a dipolar-coupled spin-1/2 network of the type 15N1-(13)C-15N2, an assessment of the sensitivity of the N --> C and C --> N TEDOR sideband intensities to the Euler angles defining the orientation of the two heteronuclear dipolar vectors in the 13C and 15N chemical shift (CS) tensor principal axes system has been carried out via numerical calculations. The results clearly indicate the potential of TEDOR MAS NMR spectroscopy for the characterization of the CS tensor orientation in the molecular frame. The efficacy of the method has been experimentally illustrated by TEDOR studies on a polycrystalline sample of [1, 3-(15)N2, 2-(13)C]uracil, which is one of the four bases in RNA.