Despite the many conveniences of Radio Frequency Identification (RFID) systems, the underlying open architecture for communication between the RFID devices may lead to various security threats. Recently, many solutions were proposed to secure RFID systems and many such systems are based on only lightweight primitives, including symmetric encryption, hash functions, and exclusive OR operation. Many solutions based on only lightweight primitives were proved insecure, whereas, due to resource-constrained nature of RFID devices, the public key-based cryptographic solutions are unenviable for RFID systems. Very recently, Gope and Hwang proposed an authentication protocol for RFID systems based on only lightweight primitives and claimed their protocol can withstand all known attacks. However, as per the analysis in this article, their protocol is infeasible and is vulnerable to collision, denial-of-service (DoS), and stolen verifier attacks. This article then presents an improved realistic and lightweight authentication protocol to ensure protection against known attacks. The security of the proposed protocol is formally analyzed using Burrows Abadi-Needham (BAN) logic and under the attack model of automated security verification tool ProVerif. Moreover, the security features are also well analyzed, although informally. The proposed protocol outperforms the competing protocols in terms of security.