In this paper, we present and evaluate a new topology for interconnection networks which we refer to as WK-pyramid. This network has a recursive definition quite similar to that of conventional pyramid networks, but is based on the WK-recursive mesh. The traditional pyramid, a desirable network topology, was employed as both software data structure and hardware architecture. However, the new network topology which we propose has, in addition to almost all the properties of the pyramid, a number of superior properties, such as expandability to any base size. We show that this hierarchical topology is of interesting topological characteristics, making it suitable for utilization as the base topology of large-scale multicomputer systems.