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Following the continuous evolution of the Internet and related technologies, distributed and collaborative networked computing systems have become one of the increasingly considered fields of research. In order to realize the cooperation of nodes in distributed systems, trustworthy group formation is required to support cooperative activities of nodes like sharing of their computing power, storage space and other resources. In distributed systems, there are no centralized information sharing schemes to provide each node with information about other nodes. Each node has to collect information about other nodes by itself and make further decisions by using the information. Thus, in order to establish efficient collaboration in a network of participants and players that might not have sufficient prior knowledge about each other, it is essential to support distributed trust management. In addition, due to dynamic and uncertain nature, distributed systems are vulnerable to numerous security threats that can adversely affect their proper functioning. Without eliminating attacks like reply-attack, denial of service attack (DoS), and other malicious activities, it is difficult to effectively compute and manage trust in distributed systems. In this paper, we discuss malicious activities of nodes and introduce an solution to make a system more trustworthy in presence of malicious nodes. Based on the trustworthiness concept, we propose a novel algorithm based on decentralized trust management concepts to compose a trustworthy group in distributed systems to support collaboration based applications.