A non-regenerative dual-hop wireless system based on distributed Alamouti space-time coding is considered. It is assumed that each relay retransmits an appropriately scaled space-time coded version of its received signal. The main goal of this paper is to find a scaling function for each relay to minimize the outage probability. In the high signal-to-noise ratio (SNR) regime for the relay-destination link, it is shown that a threshold-based scaling function (i.e., the relay remains silent if its channel gain with the source is less than its predetermined threshold) is optimum from the outage probability point of view. Numerical results demonstrate a dramatic performance improvement as compared to the case that the relay stations forward their received signals with full power even for finite SNR scenarios.