In this paper, we consider the peer-to-peer (P2P) model as a fully distributed, scalable system different from centralized coordinated systems like Cloud computing systems. A P2P system is composed of peer processes (peers). Here, applications are realized in activities and cooperation of a group of multiple peers. Since there is no centralized coordination in P2P systems, each peer has to obtain information about others by itself. In group cooperation activities, each member peer has to be trustworthy so that malicious actions of a peer cannot affect overall outcome of the whole group. It is important to consider the trustworthiness of each peer as a base of cooperation in the distributed environment. The goal of a group and the way to archive the goal are decided by the member peers. During the cooperation, opinions of each group member have to be considered. Malicious and unexpected opinions of member peers can negatively affect the output of a group. Hence, it is significant to discuss how to compose a group only by including more trustworthy peers and making less trustworthy pees not affect other peers. In this paper, by taking advantage of the trustworthiness concept of each peer, we propose a novel approach to composing a trustworthy group in the distributed agreement protocols.