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Chien et al. (2009) proposed an e-will system on the Internet using an identity-based cryptosystem. They claimed that their e-will system was secure enough to be used in practice since their system conforms to R.O.C. (Taiwan) Civil Law. However, we found several problems of Chien et al.'s scheme. First, the Trust Authority knows or can easily compute the user's private key. Therefore, it does not provide the non-repudiation property and it does not conform to the Electronic Signatures Act and the relevant regulations in the R.O.C. (Taiwan) government. Second, their scheme does not provide any long-term validation method of digital signatures. Therefore, we may fail to check the validity of the testator's will after death. To solve these problems, we propose a novel e-will system based on Government Public Key Infrastructure (GPKI) that can be used in practice.