Decentralized energy management can preserve the privacy of individual energy systems while mitigating computational and communication burdens. However, most decentralized energy management methods are partially decentralized and cannot ensure information exchange security. Therefore, this paper provides a secure fully decentralized energy management by using blockchain. First, a fully decentralized energy management framework using the optimality condition decomposition (OCD) is provided, in which individual energy system operators only exchange the boundary information with their peers rather than submitting proprietary information to a centralized system operator. Then, an asynchronous mechanism is proposed for updating the information exchange in OCD, enabling the proposed decentralized management to work under potential communication latency or interruption. Furthermore, the blockchain-based framework with state machine replication (SMR) based consensus algorithm is provided to safeguard the information exchange among individual energy systems in a secure and tamper-proof manner. The proposed decentralized energy management is tested on a multi-energy system with seven subsystems and a real-world multi-energy system in North China. The numerical results demonstrate the effectiveness of the proposed method in privacy protection and data security enhancement. The proposed method can prevent the cost increase caused by cheating activities, which in some subsystems can reach 17.6%. Additionally, the proposed fully decentralized method outperforms the partially decentralized method by 37.7% in reducing computation time. Also demonstrated are the computational precision, scalability and adaptability of the proposed method.1