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We investigate selection beamforming for a cooperative network that consists of a source, a destination, and two amplify-and-forward (AF) relays, which are all equipped with multiple antennas. The transmit and receive beamforming techniques are respectively applied at the source and destination, and the linear processing operator of the selected AF multiple-input multiple-output (MIMO) relay is optimized. We consider that the source has the instantaneous channel state information (CSI) of the channels from the source to relays but no information regarding the CSI of the channels from the relays to the destination. Partial relay selection (PRS) is employed, i.e., the source routes its information signal to the relay which offers better first-hop signal-to-noise ratio (SNR). Considering a Rayleigh fading environment, we derive an exact closed-form expression for the outage probability at the destination. The validity of the outage probability expression has been confirmed with numerical simulations. We also present the asymptotic analysis of the PRS scheme for the considered multiantenna system and derive the expressions of diversity gain. It is shown that, the overall diversity gain is min(min(nr,1nd,nr,2nd), nr,1ns +nr,2ns) where ns, nd, and nr,q are, respectively, the numbers of antennas at the source, destination and the qth relay. For the condition C : min(nr,1nd,nr,2nd) ≥ nr,1ns + nr,2ns that can be easily met with practically realizable antenna configurations, it is shown that PRS provides the same diversity order as opportunistic relaying (OR).