For the parallel tasks represented by the directed acyclic graph (DAG), if it is linearly clustered, the ordering of the execution time of the tasks in each cluster is based on their arrows in the DAG. But for nonlinearly clustering, the ordering of the independent tasks in each cluster is not easily decided. Improper ordering of these independent tasks will greatly increase the scheduling length of the DAG. We discuss the shortcomings of current scheduling algorithms and the reason behind poor performance, and then propose some new node information to be extracted which is used by a new independent tasks scheduling algorithm based on the maximized parallelism degree (MPD). Experimental results show that the MPD algorithm can yield better performance than the previous algorithms.