Checkpointing is the one of fault-tolerant techniques to restore faults and to restart job fast. Checkpointing algorithms in distributed systems have been studied for many years. These algorithms can be classified into synchronous Checkpointing algorithms and asynchronous Checkpoiting algorithms. In this paper, we propose an independent Checkpointing algorithm that has a minimum Checkpointing counts equal to periodic Checkpointing algorithm, and relatively short rollback distance at faulty situation. Checkpointing count is directly related to task completion time in a fault-free situation and short rollback distance is directly related to task completion time in a faulty situation. The proposed algorithm is compared with the previously proposed asynchronous Checkpointing algorithms using simulation. In the simulation, the proposed Checkpointing algorithm produces better results than other algorithms in terms of task completion time in fault-free as well as faulty situations.