Current Web authentication frameworks have well-known weaknesses. HTTP provides an access authentication framework, but it is rarely used because it lacks presentational control. Forms and cookies, which are most commonly used, have the long-standing privacy issue raised by tracking. URI sessions, which are used in some mobile services like i-mode 1.0, disclose session identifiers unintentionally. This paper proposes iAuth, which integrates better parts of the existing frameworks and fixes their problems; iAuth allows servers to provide log-in forms, and introduces a session header to avoid servers' tracking and unintentional disclosure. Since iAuth has backward compatibility with the major legacy browsers, developers can freely introduce iAuth into their Web sites or browsers as needed. Experiments confirm its correct operation; an iAuth server is shown to support not only an iAuth client but major legacy browsers. We believe that iAuth will resolve the long-standing issues in Web authentication.