This paper investigates orthogonal space-time block code (OSTBC) transmission for multiple-input multiple-output (MIMO) amplify-and-forward (AF) relaying networks composed of one source, K relays, and one destination and with M-ary frequency-shift keying (FSK) modulation. A non-coherent detection scheme is proposed and analyzed in a situation where the fading channels undergo temporal correlation. Specifically, by properly exploiting the implicit pilot-symbol-assist property of FSK transmission, the destination estimates the overall channels based on the linear minimum mean square error (LMMSE) estimation algorithm. It then utilizes the maximal ratio combining (MRC) to detect the transmitted information. An upper bound on the probability of errors is derived for a network with arbitrary numbers of transceiver antennas and relays. Based on the obtained bit error rate, the full achievable diversity order is verified. Simulation results are presented to show the validity of the analytical results.