Data declustering methods of parallel databases have significant effect on the performance of the parallel algorithms on the databases. If the characteristics of the declustering methods of the parallel database can be adequately exploited in designing parallel algorithms for implementing the database operations in parallel database systems, high performance parallel algorithms could be resulted. Unfortunately, the advantages of the underlying declustering methods of the parallel databases are rarely considered in existent parallel algorithms on the parallel databases. The focus of this paper is on how to utilize the advantages of the underlying declustering methods of the databases in designing parallel join algorithms. A set of parallel join algorithms based on the CMD declustering method are proposed. Theoretical and experimental results show that the proposed algorithms are more efficient than other parallel join algorithms.