With the improvement of satellite autonomy, multi-satellite cooperative mission planning has become an important application. This requires multiple satellites to interact with each other via inter-satellite links to reach a consistent mission planning scheme. Considering issues such as inter-satellite link failure, external interference, and communication delay, algorithms should minimize communication costs as much as possible. The CBBA algorithm belongs to a fully distributed multi-agent task allocation algorithm, which has been introduced into multi-satellite autonomous task planning scenarios and achieved good planning results. This paper mainly focuses on the communication problem, and proposes an improved algorithm based on it, which is called c-CBBA. The algorithm is designed with task preemption strategy and single-chain strategy to reduce the communication volume. The task preemption strategy is an accelerated convergence mechanism designed for the convergence characteristics of CBBA, while the single-chain strategy is a communication link pruning strategy designed for the information exchange characteristics of satellites. Experiments in various scenarios show that the algorithm can effectively reduce communication volume while ensuring the effectiveness of task planning.