Energy harvesting (EH) is an attractive solution to prolong the lifetime of wireless devices. With EH capability, an intermediate node, acting as the relay, can extract energy from the signal of a source node and use the harvested energy to perform information relaying, enabling a self-sustainable cooperative network. To efficiently use the harvested energy, it is important to select proper relays to receive and forward the source signal. In this paper, we investigate the relay selection (RS) problem for EH relays with short-term energy storage. A relay selection scheme, called selective max-max relay selection (S-MMRS), is proposed aiming to exploit diversity gain that is not achieved in the previous work. To evaluate the performance of S-MMRS, we theoretically analyze its outage probability. Simulation results are presented to verify the analysis accuracy and demonstrate that S-MMRS is a diversity achievable scheme.