In order to fulfill the increasing demand for computation power to process a boundless data concurrently within a very short time or real-time in many areas such as IoT, AI, machine learning, smart grid, and big data analytics, we need exa-scale or zetta-scale computation in the near future. Thus, to have this level of computation, we need a massively parallel computer (MPC) system that shall consist of millions of nodes; and, for the interconnection of these massive numbers of nodes, conventional topologies are infeasible. Thus, a hierarchical interconnection network (HIN) is a rational way to connect huge nodes. Through this article, we are proposing a new HIN, which is a tori-connected flattened butterfly network (TFBN) for the next generation MPC system. Numerous basic modules are hierarchically interconnected as a toroidal connection, whereby the basic modules are flattened butterfly networks. We have studied the network architecture, static network performance, and static cost-effectiveness of the proposed TFBN in detail; and compared static network and cost-effectiveness performance of the TFBN to those of TTN, torus, TESH, and mesh networks. It is depicted that TFBN possesses low diameter and average distance, high arc connectivity, and temperate bisection width. It also has better cost-effectiveness and cost-performance trade-off factor compared to those of TTN, torus, TESH, and mesh networks. The only shortcoming is that the complexity of wiring of the TFBN is higher than that of those networks; this is because the basic module necessitates some extra short length link to form the flattened butterfly network. Therefore, TFBN is a high performance and cost-effective HIN, and it will be a good option for the next generation MPC system.