In cloud storage, the third-party auditor (TPA) will perform public auditing and data integrity check to maintain the integrity of outsourced data stored in the cloud server. To avoid possible user privacy leakage in the auditing process, the TPA should learn nothing about the user. This paper presents a new auditing scheme which can keep the TPA from learning any user data block in an earlier stage in contrast to previous schemes. Simulation runs are carried out to examine the privacy preserving performance of our new scheme and related schemes. The results show that our scheme is able to produce better privacy protection at no more computation time cost for involved entities, i.e., the user, server and TPA.