Public auditing is an important issue in cloud storage service because a cloud service provider may try to hide management mistakes and system errors from users or even steal or tamper with a user’s data for monetary reasons. Without the protection of a proper auditing mechanism, cloud users would have to run high risks of having their legal rights and interests spoiled without their knowledge. Therefore, many data integrity, assurance, and correctness schemes have been proposed for data auditing. Most of these schemes work by randomly sampling and aggregating signatures from bilinear maps (for more efficiency) to check whether the cloud storage service is honest and whether the data stored in the cloud is correct. Although aggregating signatures can reduce the auditor’s computing overhead and time, unfortunately, none of these schemes have offered any workable solution to giving detailed information on where the errors are when the cloud data as a whole fails the auditing. To fix this problem, we shall propose a new public auditing scheme with a mechanism integrated into it especially to locate the problematic data blocks when they exist. With efficiency, the proposed scheme is capable not only of giving an accurate pass/fail report but also providing detailed information on the locations of the errors detected.