The authors evaluate the outage probability of a cognitive amplify-and-forward relay network with cooperation between certain secondary users, chosen by single and multi-relay (two and four) selection, based on the underlay approach, which requires adherence to an interference constraint on the primary user. The relay selection is performed either on the basis of a max-min strategy or one based on maximising exactly the end-to-end signal-to-noise ratio. To realise the relay selection schemes within the secondary networks, a predetermined threshold for the power of the received signal in the primary receiver is assumed. To assess the performance advantage of adding additional secondary relays, we obtain analytical expressions for the probability density function and cumulative density function of the received SNR and thereby provide closed form and near closed form expressions for outage probability over Rayleigh frequency flat fading channels. In particular, the authors present lower and upper bound expressions for outage probability and then provide a new exact expression for outage probability. These analytical results are verified by numerical simulation.