Sufficient conditions (in terms of restrictions on individual preferences) have been already established in the literature for transitivity of simple majority decisions when individual preferences are quasi-transitive (but not necessarily transitive) and also for transitivity of multi-stage majority decisions when individual preferences are transitive. This paper establishes sufficient conditions for transitivity of multi-stage majority decisions when individual preferences are quasi-transitive, but not necessarily transitive. This constitutes a generalization of several results proved earlier.