This paper describes an efficient implementation of MPI on the Memory-Based Communication Facilities; Memory-Based FIFO is used for buffering by the library, and Remote Write for communication with no buffering. The Memory-Based Communication Facilities are software-based communication mechanisms, with off-the-shelf Ethernet hardware. They provide low-cost and highly-functional primitives for remote memory accesses. The performance of the library was evaluated on a cluster of workstations connected with a 100Base-TX network. The round-trip time was 71 us for 0 byte message, and the peak bandwidth was 11.86 Mbyte/s in full-duplex mode. These values show that it is more efficient to realize the message passing libraries with the shared memory model than with the message passing model.