The theory and experimental observation of the third-order effect in solid-state NMR of quadrupolar nuclei are presented. The third-order effect consists of spherical harmonic terms up to rank l=6 and shifts NMR frequencies between two spin states that are not symmetric such as satellite transitions. Two-dimensional satellite transition magic-angle spinning experiment averages both the first and the second-order quadrupolar interactions making the quantitative measurement of the third-order effect possible. The third-order quadrupolar effect in andalusite has been measured at 11.7 T and its powder patterns are fitted with numerical simulations.