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This paper proposes a three-dimensional (3-D) geometry-based three-cylinder scattering model for multiple-input-multiple-output (MIMO) mobile-to-mobile (M2M) fading channels in relay-based amplify-and-forward (AF) cooperative networks. Non-line-of-sight (NLoS) propagation conditions are assumed in the transmission links from the source mobile station to the mobile relay station and then to the destination mobile station. Based on the three-cylinder model, a 3-D reference model for narrowband MIMO M2M relay fading channels is derived. From the reference model, analytical and closed-form solutions are provided for the four-dimensional (4-D) space-time correlation function (STCF), under non-isotropic scattering conditions. Numerical calculations demonstrate the theoretical derivations.