In hierarchical classification, the prediction paths may be required to always end at leaf nodes. This is called mandatory leaf node prediction (MLNP) and is particularly useful when the leaf nodes have much stronger semantic meaning than the internal nodes. However, while there have been a lot of MLNP methods in hierarchical multiclass classification, performing MLNP in hierarchical multilabel classification is much more difficult. In this paper, we propose a novel MLNP algorithm that (i) considers the global hierarchy structure; and (ii) can be used on hierarchies of both trees and DAGs. We show that one can efficiently maximize the joint posterior probability of all the node labels by a simple greedy algorithm. Moreover, this can be further extended to the minimization of the expected symmetric loss. Experiments are performed on a number of real-world data sets with tree- and DAG-structured label hierarchies. The proposed method consistently outperforms other hierarchical and flat multilabel classification methods.