We study a new relay selection scheme in nonregenerative relay networks consisting of a source, a destination, an eavesdropper, and multiple relays, where each terminal has a single antenna and operates in a half duplex mode. In these networks, it is desirable to protect the confidential message from the source to the destination against the eavesdropper with the help of a single selected relay. Specifically, we begin by investigating one scenario: instantaneous signal to noise ratios (SNRs) related to the eavesdropper are available. For the scenario, we propose relay selection to maximize the secrecy capacity of nonregenerative networks with and without direct paths. For networks with direct-paths, we derive a closed-form approximation of the secrecy outage probability. As a special case, for networks without direct-paths, we derive the exact secrecy outage probability expression in integral form and offer as well a closed-form approximation. © 2014 IEEE.