We have performed two-pulse and three-pulse time-integrated as well as spectrally resolved four-wave-mixing measurements on a single CdMnTe/CdTe/CdMgTe quantum well. The polarization dependence of both four-wave-mixing measurements can be explained well by the five-level model of the exciton-biexciton system including two-biexciton states with parallel spin and anti-parallel spin orientations.