Best relay selection (BRS) is crucial in enhancing the performance of cooperative networks. In contrast to most previous works, where the guidelines for BRS are limited to Gaussian noise, in this article, we propose a novel relay selection protocol for a decode-and-forward cooperative network taking into account the bursty impulsive noise (IN). The proposed protocol chooses the N'th best relay considering both the channel gains and the states of the IN of the source-relay and relay-destination links. For this scheme, to obtain the state of IN, we propose a state detection algorithm using maximum a posteriori (MAP) detection. To analyze the performance of the proposed protocol, we first derive closed-form expressions for the probability density function (PDF) of the received signal-to-noise ratio assuming all the relays know the state of IN perfectly (genie-condition). Then, these PDFs are used to derive closed-form expressions for the bit error rate (BER) and the outage probability. Finally, we also derive the asymptotic BER and outage expressions to quantify the diversity benefits. We show that the proposed MAP-based N'th BRS protocol attains the derived genie-aided analytical results and outperforms the conventional relay selection protocol, optimized for the Gaussian case, and which does not take into account the IN memory.