Parallel systems for OPS5 have been developed. In such systems, parallel implementations of the Rete algorithm are adopted because the number of pattern matchings is minimized in the original algorithm. However, conventional approaches for parallel Rete algorithms require special hardware to cope with the dynamic process allocation and frequent communication. Dedicated machines are necessary for such methods. In this paper, a new parallel execution method for general purpose multiprocessors is proposed. In this method, nodes in the Rete network are statically mapped onto a small number of processors (PUs) before execution. Since processes are not migrated and are not allocated dynamically, data structures can be designed so as to minimize the communication between PUs. Also the synchronization and process control can be simplified. The key for the method is static mapping algorithms. Since the characteristics of the Rete network are completely different from the data dependency graph which is suitable for extracting inherent parallelism in general programming languages like FORTRAN, the conventional static mapping techniques cannot be applied. Some new mapping strategies are discussed and evaluated. Although the method is utilized for most types of multiprocessors, an optimized architecture which is called MANJI-II is designed and proposed. MANJI-II supports quick transfer of tokens in the Rete network, by using a simple multicast mechanism, and non-cached shared memory. Although MANJI-II provides almost the same performance as that of dedicated architecture including the previous version of MANJI, the total cost of MANJI-II is extremely low.