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This Radio Frequency Identification (RFID) systems suffer from different security and privacy problems, among which relay attack is a hot topic recently. A relay attack is a type of attack related to man-in-the-middle and replay attacks, in which an attacker relays verbatim a message from the sender to a valid receiver of the message. The sender may not be aware of even sending the message to the attacker. The main countermeasure against relay attack is the use of distance bounding protocols measuring the round-trip time between the reader and the tag. In this paper, we consider a modification of these protocols using `error state' which stands for the number of response bit errors that have already occurred. We set a maximal error number to prevent adversary from malicious queries, we also apply a punishment mechanism for error responding, which to my best knowledge is proposed at the first time in distance bounding protocols, if the tag sends one error bit, it should respond one more challenge bit to successfully finish the protocol. By using error state and punishment mechanism, the success probability for an adversary to access to the system decreases. Finally, we use the Hancke and Kuhn's protocol as a comparison, to show the improvements achieved when different cases are analyzed.