Multi – stage group testing design involves testing groups for the presence or absence of traits in a population and sequentially subdividing the groups into sub – groups. The sub – groups to be tested at a particular stage are based on the information obtained from the previous stage. This paper developed an M – stage design for testing the presence of multiple traits in a finite population. The asymptotic variance of the model is also discussed. The model gains efficiency with each additional stage when the occurrence of traits is rare in the population.