A client stores data in the cloud and uses remote data checking (RDC) schemes to check the integrity of the data. The client can detect the corruption of the data using RDC schemes. Recently, robust RDC schemes have integrated forward error-correcting codes (FECs) to ensure the integrity of data while enabling dynamic update operations. Thus, minor data corruption can be recovered by FECs, whereas major data corruption can be detected by spot-checking techniques. However, this requires high communication overhead for dynamic update, because a small update may require the client to download an entire file. The Variable Length Constraint Group (VLCG) scheme overcomes this disadvantage by downloading the RS-encoded parity data for update instead of the entire file. Despite this, it needs to download all the parity data for any minor update. In this paper, we propose an improved RDC scheme in which the communication overhead can be reduced by downloading only a part of the parity data for update while simultaneously ensuring the integrity of the data. Efficiency and security analysis show that the proposed scheme enhances efficiency without any security degradation.