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An approach to the determination of the 2-(13)C' chemical shift (CS) tensor orientation in pyrimidine bases via heteronuclear MAS NMR spectroscopy is presented. Considering a dipolar coupled spin 1/2 network of the type S1-I-S2 consisting of directly bonded heteronuclear spins, we have carried out numerical simulations to assess the sensitivity of I-S REDOR spinning sidebands to the Euler angles defining the orientation of the I-S1 and I-S2 dipolar vectors in the I spin CS tensor principal axes system. Our investigations clearly demonstrate the potential of I-S REDOR studies in IS1S2 systems for obtaining with high reliability and accuracy the I spin chemical shift tensor orientation in the molecular frame spanned by the two internuclear vectors I-S1 and I-S2. The significant contribution to the observed REDOR sideband intensities from anti-phase operator terms which are present at the start of the data acquisition is illustrated. The procedure for the recording and analysis of the I-S REDOR spectra in IS1S2 systems is presented and the measurement of the 2-(13)C' CS tensor orientation in a polycrystalline sample of [1,3-(15)N2, 2-(13)C] uracil, which is one of the four bases in RNA, is experimentally demonstrated.