The combined effect of the tensorial interactions from both second-order quadrupole coupling and chemical shielding on the central transition in magic-angle spinning (MAS) NMR of half-integer quadrupolar nuclei has been convincingly observed and analyzed for the first time. Rb-87 MAS NMR spectra of RbClO4 at 7.1, 9.4, and 11.7 T and at different spinning speeds serve as the illustrative example. The spectra are analyzed by iterative fitting of their complex line shapes using a modification of our simulation software recently described and employed for determination of the same two interactions from first-order MAS NMR spectra of all (central and satellite) transitions. Accurate and consistent values for the eight parameters describing the magnitudes and relative orientation of the two tenser interactions are obtained from the different spectra. The parameters determined from Rb-87 MAS NMR are of higher accuracy than the values earlier reported from static-powder Rb-87 NMR of RbClO4. The relative orientation (Euler angles psi, chi, and xi) determined for the two tensorial interactions conforms to the crystal structure for RbClO4 in an excellent manner.