The correlation between the direction of propagation of one quantum and the polarization of another quantum, when the two are emitted successively (in any order) by a radiating system, is investigated theoretically. This direction-polarization correlation is found to be capable of determining the relative parities of all three levels of the radiating system. The correlation is simply related to the already investigated correlation between the directions of propagation of two successive quanta. Results are given explicitly for the possible combinations of dipole and quadrupole radiation. The discussion applies also to certain types of resonance radiation.