In recent work, Yan et al. designed an auditing protocol with a designated verifier. Note that, Yan et al.'s protocol suffers from great communication redundancy. In order to reduce it, a flexible and improved scheme is proposed, which tries to "aggregate" the tags of multiple data segments and thus greatly reduces the communication overhead. Meanwhile, we give the security proof based on the computational Diffie-Hellman assumption. A concrete example shows that the communication overhead of the improved protocol can be greatly reduced.