In this paper, we consider an underlay secondary network comprising of K transmitter-receiver pairs sharing the spectrum of a primary network, which is divided into n non-overlapping frequency bands (subchannels). Each secondary pair can communicate over only one subchannel and should keep the interference generated to the primary network below a threshold. A decentralized multiple access algorithm is used by the secondary pairs to select a proper subchannel. We study the performance of a modified version of the medium access control (MAC) protocol proposed by Elkashlan et al., referred to as the general order selection algorithm. We obtain the statistics of the output signal-to-noise ratio of the algorithm, and the statistics of the achievable capacity per secondary pair. Closed-form expressions for the outage probability, average bit error rate of the secondary users, and the aggregate throughput of the secondary network are derived. Assessment of the analytical work of this paper is done through comparisons with simulation.