We propose a series of heteronuclear dipolar recoupling schemes which are insensitive to the presence of homonuclear dipolar interaction. The schemes are based on the pulse symmetry CNnnu. The optimum choices for N, n, and nu were determined with the help of Average Hamiltonian Theory (AHT). The lowest-order AHT shows that the pulse symmetries with n=N and nu =1 are suitable for the recoupling of heteronuclear dipolar interactions. Together with the parabolic approximation of the dephasing curve, we develop a powerful experimental strategy to characterize the van Vleck's second moments for multiple-spin systems under conditions of very fast magic-angle spinning. These new pulse symmetries are superior to the rotational echo double resonance (REDOR) method and other recoupling schemes as far as the interference of the homonuclear dipolar interaction is concerned. Preliminary experimental results on crystalline model compounds are given to illustrate the utility of our approach.