The problem of definite information leakage existing in the controlled bidirectional quantum direct communication protocol using GHZ states [Chin. Phys. Lett. 23 (2006) 1680
] was pointed out by Ye and Jiang [Chin. Phys. Lett. 30 (2013) 040305
]. Then, they proposed two strategies to improve this security bug. However, if the revised versions are analyzed from the viewpoint of information theory, it can be found that they still have the problem of information leakage. That is, three quarters and one half of the information interchanged by the communication parties are leaked out unknowingly in the first and second revised protocols, respectively.