Cloud auditing with ownership transfer is a provable data possession scheme meeting verifiability and transferability simultaneously. In particular, not only cloud data can be transferred to other cloud clients, but also tags for integrity verification can be transferred to new data owners. More concretely, it requires that tags belonging to the old owner can be transformed into that of the new owner by replacing the secret key for tag generation while verifiability still remains. We found that existing solutions are less efficient due to the huge communication overhead linear with the number of tags. In this paper, we propose a secure auditing protocol with efficient ownership transfer for cloud data. Specifically, we sharply reduce the communication overhead produced by ownership transfer to be independent of the number of tags, making it with a constant size. Meanwhile, the computational cost during this process on both transfer parties is constant as well.