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The notion of Public Key Encryption with Keyword Search (PEKS), which enables one to search encrypted data in public key setting, was firstly suggested by Boneh et al. in 2004. So far most of presented PEKS schemes were constructed based on bilinear pairing. However, PEKS schemes based on pairing are susceptible to off-line keyword guessing attacks. In ICCSA 2006, Khader proposed a PEKS scheme not using pairing. In this paper, we show that Khader' scheme do not satisfy the consistency which is necessary for a PEKS scheme to fulfill its functionality. Then, we propose a variant of Khader scheme which is not only computationally consistent but also greatly improves efficiency.