Peer-to-peer systems are prone to faults, thus it is vitally important to design peer-to-peer systems to automatically regain consistency, namely to be self-stabilizing. Toward this goal, we present a deterministic structure that defines for every n the entire (IP) pointers structure among the n machines. Namely, the next hop for the insert, delete and search procedures of the peer-to-peer system. Thus, the consistency of the system is easily defined, monitored, verified and repaired. We present the HyperTree (distributed) structure which support the peer-to-peer procedures while ensuring that the out-degree and in-degree (the number of outgoing/incoming pointers) are b\log _b N where N in the maximal number of machines and b is an integer parameter greater than 1. In addition the HyperTree ensures that the maximal number of hops involved in each procedure is bounded by b\log _b N. A self-stabilizing peer-to-peer system based on the HyperTree is presented.