Wireless Body Area Networks (WBANs) connects a variety of sensor nodes that operate in close vicinity to, on or inside a human body. Recently, the IEEE Task Group 6 has established the first international WBANs standard, called IEEE 802.15.6. Since some communications can carry sensitive information, the standard provides for strong security by a security association procedure that identifies WBANs’ nodes and the Body Network Coordinator (BNC) to each other. However, many security vulnerabilities are noticed in the above procedure, especially to the Key Compromise Impersonation (KCI) and the Impersonation attacks. In this paper, we design a secure key management and nodes authentication scheme, called Server-Based Secure Key Management for the IEEE 802.15.6 standard (SBSKM). The objective of the proposed scheme is to improve the IEEE 802.15.6 security by ensuring the encryption of all communications, starting from the beginning of the security association procedure. To that, we extended the security architecture of the standard with a trusted server, responsible for the creation, initialization, and distribution of encryption keys as well as guarantee of the identity of the sensor nodes joining the network. Over Castalia simulator based on OMNeT++, expanded simulations have been performed and the results show the robustness of our solution which, on the one hand, allowed us to overcome the lack of authentication and confidentiality in the standard security scheme, and on the other hand, it doesn’t lead to a reduction in the standard's performances.