The asynchronous Byzantine fault tolerant (BFT) protocol has emerged as a reliable service infrastructure for permissioned blockchains due to its powerful fault tolerance and robustness. HoneyBadgerBFT is the first practical asynchronous BFT consensus protocol that utilizes reliable broadcast (RB) and asynchronous binary agreement (ABA) to construct asynchronous common subsets (ACS), which guarantees liveness without making any timing assumptions. While HoneyBadgerBFT claims to achieve asymptotic optimal efficiency, its reliance on concurrent execution of n ABA instances introduces \(O(\textbf{log}\ n)\) time complexity. The subsequently proposed Dumbo protocol optimizes the number of ABA instances. Dumbo1 reduces the ABA instances to \(\kappa \) ones independent of n; and Dumbo2 reduces the ABA instances to a constant, but is still expected to run three consecutive ABA instances. To address this limitation, this paper designs a variant of the ABA protocol, random asynchronous binary agreement (RdABA), and constructs the RdBFT protocol, which reduces the expected number of ABA instances to 1.5. To further enhance the throughput, this paper constructs the chained-RdBFT protocol, which introduces cross-epoch indexing, with only one ABA instance running in each epoch. This paper proves the security and liveness of the proposed protocol in asynchronous model and verifies its efficiency through experiment evaluation.