In this paper, the new detection scheme proposed by Tarokh and Alamouti is investigated and expanded to two schemes of two transmit two receive antennas and four transmit one receive antennas. Previously, Tarokh and Alamouti, based on the simple transmit diversity scheme proposed by Alamouti, have provided two new detection methods to decode signals at the receiver without channel information. We expand their work to two and four transmit antennas with different number of receive antennas. We also demonstrate that the two methods are in fact the same with one being a special case of the other. The theory and detailed derivation of detection formulas for three cases, Tarokh and Alamouti work, two transmit two receive antennas and four transmit one receive antennas are presented.