Wireless telecommunications systems have expanded rapidly over the past few years. Wireless Body Sensor Network (WBSN) is a relatively novel area of research and development in healthcare systems. However, it has multiple constraints and challenges regarding human health, social interactions, coverage radius, energy consumption, and communication reliability. In addition, communications between nodes can contain highly sensitive personal information, while hostile environments will impose a wide range of security risks. Therefore, designing authenticated key agreement (AKA) protocols is a crucial challenge in these networks. The current study, considering the security issues of the Li et al. scheme and some of their new extensions, proposes an improved AKA protocol with anonymity and unlinkability of the sensor node sessions. The results of theoretical analysis compared with similar schemes indicated that the proposed scheme could reduce average energy consumption and communication cost by 41 percent. It also reduced the average computation time by 61 percent. Furthermore, it was shown by formal/informal analyses that, on top of unlinkability and anonymity features, other central security features in the current scheme were similar and comparable to those in the recent and similar schemes.