The block layered space-time codes, with the intent of simultaneously achieving high coding gain and high code rate, have been suggested. These codes are based on the design mechanisms of existing layered space-time codes and space-time block codes. The previously known concept of a layer has been modified to a block layer wherein a block layer has more than one antenna transmitting at the same instant and hence the name for this scheme. The role of the layers is to provide multiplexing. Each block layer incorporates Alamouti's transmit diversity scheme which decreases the decoding complexity and the component Alamouti codes are built on rotated constellations. The block layers are made transparent to each other by Diophantine approximation. The use of space-time codes improves the coding gain for the suggested code design scheme. This scheme has been implemented for four transmit antennas and four receive antennas but can easily be extended to any number of antennas depending on the code rate desired. The proposed codes achieve a normalized rate of 2-symbol/s. Simulation results show that the block layered space-time codes outperform threaded algebraic space-time (TAST) codes in certain scenarios