RFID is popular to be used in plenty of applications with its capability of remote automatic identification. However, information transmitted wirelessly is under the treats of eavesdropping, interception, or modification because of the nature of the transmission media. Thus, Yeh et al. proposed an RFID authentication scheme based on quadratic residues by improving Chen et al.'s. However, we find that the server needs to maintain the obsolete shared secret key to resist DoS (Denial of Service) attack in both schemes. To overcome this drawback and improve the computation load, an improvement will be given with simple operations, one-way hash function and XOR operations. The proposed scheme can defend against possible attacks and be suitable for applications requiring efficiency and security at the same time.