An approach to the determination of the orientation of the carbonyl chemical shift (CS) tensor in a 13C-15N-1H dipolar coupled spin network is proposed. The method involves the measurement of the Euler angles of the 13C'-15N and 15N-1H dipolar vectors in the 13C' CS tensor principal axes system, respectively, via a 13C-15N REDOR experiment and by a 2D relayed anisotropy correlation of the 13C' CSA (omega2) and 15N-1H dipolar interaction (omega1). Via numerical simulations the sensitivity of the omega1 cross sections of the 2D spectrum to the Euler angles of the 15N-1H bond vector in the 13C' CSA frame is shown. Employing the procedure outlined in this work, we have determined the orientation of the 13C' CS tensor in the peptide plane of the dipeptide AibAib-NH2 (Aib = alpha-aminoisobutyric acid). The Euler angles are found to be (chiCN, psiCN) = (34 degrees +/- 2 degrees, 88 degrees +/- 2 degrees) and (chiNH, psiNH) = (90 degrees +/- 10 degrees, 80 degrees +/- 10 degrees). From the measured Euler angles it is seen that the sigma33 and sigma22 components of the 13C' CS tensor approximately lie in the peptide plane.