In this paper, we analyze the performance of the 21 Alamouti scheme suggested by Alamouti, composed of the transmit space-time code and the simple linear decoding processing, in perfectly time-varying and spatially correlated channels. We derive the closed-form probability density function (PDF) of output signal-to-noise ratio (SNR) and outage probability of the Alamouti scheme as a function of spatial correlation coefficient in the consideration of no correlation in time. We observe that the performance of the Alamouti scheme is severely degraded when the channels are time-varying and spatially correlated.