In this paper, we consider a multi-relay network operating in decode-and-forward mode. We propose a novel relay selection method with a low implementation complexity. Unlike the competing schemes, it requires neither error detection methods at relay nodes nor feedback information at the source. Our proposed selection method is able to extract the full diversity. We further formulate a power allocation strategy to minimize the symbol error rate which brings further improvements over the equal power allocation among the source and relay nodes. Extensive Monte Carlo simulations are also presented to compare the performance of the proposed scheme with its competitors. Our proposed relay selection method outperforms competing schemes and is able to perform within 0.3 dB of the genie performance bound.