A new high-rate space-time block code (STBC) with full transmit diversity gain for four transmit antennas based on a generalized Alamouti code structure is proposed. The proposed code has lower Maximum Likelihood (ML) decoding complexity than the Double ABBA scheme does. Constellation rotation is used to maximize the diversity product. With the optimal rotated constellations, the proposed code significantly outperforms some known high-rate STBCs in the literature with similar complexity and the same spectral efficiency.