Security is an important aspect for the future wire- less networks. Since the number of network nodes increases con- stantly, and, in addition, the networks are decentralized and ad- hoc in nature, it becomes more challenging to apply the current cryptographic methods that require exchange of keys between the communicating parties. Information-theoretic secrecy is an emerging security field that explores the possibility of achieving perfect secrecy data transmission between the intended network nodes, while possible malicious nodes (also called eavesdroppers) are kept ignorant of the transmitted information. In other words, that is the ability of the physical layer to provide security (beside the reliability) of the transmitted (broadcasted) data. For that reason, it is often called physical layer security. In this paper we observe how a simple cooperative network with one relay node can improve the physical layer security by decreasing the area in which the eavesdropper can reside and listen to the information transmitted to the destination. This region is called vulnerability region and we provide its characterization. Under certain conditions, the vulnerability region vanishes, which makes our wireless system perfectly secure for any position of the eavesdropper within the wireless network.