Multiple-input multiple-output (MIMO) Beamforming (BF) performance is analyzed for amplify-and-forward (AF) fixed two-hop relay networks in independent and identically distributed (i.i.d.) Rayleigh fading channels. A novel performance bound using a new symbol-error-rate (SER) approximation is presented for AF relay networks equipped with multiple antennas at the source, relay, and destination when the channel state information (CSI) of the relay link is known at the source and destination. High signal-to-noise ratio (SNR) performance bound is also analyzed to simplify the performance via diversity and array gain expressions. Finally, the novel performance bound is compared with the optimized BF performance to show the tightness of the bound.