Alamouti codes have been widely recognized for their full-diversity performance, while they provide a symbol rate of one with symbol-by-symbol decoding complexity. To decode an Alamouti code, the receiver requires the channel state information (CSI), while the transmitter operates blindly without CSI. This paper investigates the dual scenario when CSI is available only at the transmitter and not at the receiver. Such an assumption is valid for time-division duplex (TDD) systems where the transmitter obtains the CSI from the reciprocal channel and the receiver does not want to estimate the channel because of complexity. We propose dual Alamouti codes that do not require CSI at the receiver and exploit transmit CSI to achieve the performance of full-diversity with rate-one and symbol-by-symbol decoding complexity. Moreover, the dual codes provide the same bit error rate (BER) performance as the original Alamouti codes for equal-energy constellations. The dual Alamouti codes have potential applications in TDD systems to save the cost of training and simplify receiver design.