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Cloud computing is Internet-based computing, whereby shared resources, software, and information are provided to users on demand. In general, the users of cloud computing do not own the physical infrastructure, instead avoiding capital expenditure by renting usage from a third-party provider. They consume resources as a service and pay only for resources that they use. However, there are many applications running synchronously in the service platform of cloud computing. The agreement problem is a fundamental issue of reliable distributed systems. Nevertheless, all previous studies of the agreement problem were visited in a network topology with faulty hardware components. However, in a cloud computing, there are a lot of application processes to provide the services of users. In addition, the influence of faulty process is different with the influence of faulty hardware component. Therefore, previous protocols for the agreement problem are not suitable for a cloud computing with fallible processes. To enhance the reliability, the agreement problem in a cloud computing with fallible processes is revisited in this study. The proposed protocol can solve the agreement problem with a minimal number of rounds of message exchange and tolerates a maximal number of faulty processes.