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New union bounds are derived for space-time block coded systems over Rayleigh fading channels. Both maximal ratio combining and generalised selection combining are considered as combining schemes at the receiver. The union bounds are easy to be evaluated using the transfer function of the code. Furthermore, the bounds are general to any coding scheme with a known weight distribution. Results show that the proposed union bounds are tight to simulation results for wide ranges of diversity orders and signal-to-noise ratio values.