Before an application modelled as a directed acyclic graph (DAG) is executed on a heterogeneous system, a DAG mapping policy is often enacted. After mapping, the tasks (in the DAG-based application) to be executed at each computational resource are determined. The tasks are then sent to the corresponding resources, where they are orchestrated in the pre-designed pattern to complete the work. Most DAG mapping policies in the literature assume that each computational resource is a processing node of a single processor, i.e. the tasks mapped to a resource are to be run in sequence. Our studies demonstrate that if the resource is actually a cluster with multiple processing nodes, this assumption will cause a mis-perception in the tasks' execution time and execution order. This will disturb the pre-designed cooperation among tasks so that the expected performance cannot be achieved. In this paper, a DAG mapping algorithm is presented for multicluster architectures. Each constituent cluster in the multicluster is shared by background workload (from other users) and has its own independent local scheduler. The multicluster DAG mapping policy is based on theoretical analysis and its performance is evaluated through extensive experimental studies. The results show that compared with conventional DAG mapping policies, the new scheme that we present can significantly improve the scheduling performance of a DAG-based application in terms of the schedule length.