In Japan, the revised Personal Information Protection Act is enacted in full force on May 30, 2016. It became possible to provide personal information to third parties under certain conditions such as anonymization without user agreements. However, in the case of no limitation on background knowledge of attackers, complete anonymization maintaining usability of data is impossible in principle. It is difficult to establish a rational anonymous processing standard. In this paper, an anonymization method based on residuals to establish both anonymity and usability is proposed. Moreover, it is shown that to apply anonymization with ambiguous purpose of use is meaningless.