In this paper, we consider the distributed Alamouti code for a cooperative diversity network consisting of a source, a non-regenerative relay, and a destination. While in the first time phase, the source radiates signals to both relay and destination; in the second time phase, the source and the relay cooperatively send signals to the destination by using an Alamouti code. Considering the amplify-and-forward protocol and independent Rayleigh fading, we first derive the exact average bit error rate performance in a single integral expression so that the system performance can be numerically evaluated. Then, based on a new approximation method of the Marcum Q-function, we also give a tight upper bound for the system performance with a summation of a number of series components. We demonstrate through simulation that, in various operation scenarios with different channel quality and types of modulation, the results of the exact bit error rate expression accurately matches the simulation results, and the bound is tighter and more robust than existing approximation methods. Finally, we show that the analytic work also provides a method for the optimal allocation of power between the source and the relay in the second time phase. Copyright © 2013 John Wiley & Sons, Ltd.