The frequency spectrum available for the wireless communication is extremely crowded. In order to improve the spectral efficiency, the two-way relay networks have aroused great attention. A simple $N^{th}$ best-relay selection criterion for the opportunistic two-way relay networks is proposed, which can be implemented easily by extending the distributed timer technique in practice, since the proposed criterion is mainly based on the channel gains. The outage performance of the proposed relay selection scheme is analyzed under the outdated channel state information (CSI), and a tight closed-form lower bound and asymptotic value of the outage probability over Rayleigh fading channels are obtained. Simulation results demonstrate that the tight closed-form lower bound of the outage probability very closely matches with simulated ones in the whole SNR region, and the asymptotic results provide good tight approximations to the simulation ones, especially in the high SNR region.