Magnetic-dipole two-photon absorption (MD-TPA) is introduced as a new spectroscopic technique for the study of odd-parity states. Contrary to the classical electric-dipole two-photon absorption (ED-TPA), where only spin-allowed even-parity transitions can be excited, MD-TPA allows us to excite spin-forbidden odd-parity states. This new technique is therefore very well suited to study paraexcitons in semiconductors and insulators. As examples MD-TPA measurements of RbI, NaI, and NaBr are presented.