A novel space-time block coding (STBC) scheme for four transmit antennas is proposed based on the binary phase shift keying (BPSK) constellation modulation. The new scheme achieves full diversity full rate. And it also can achieve linear decoding at receiver, so the decoding complexity at receiver is greatly reduced. Because the scheme can achieve full diversity, good performance can be obtained not only at low signal to noise ratio (SNR) but also at high SNR. To improve the code rate further, we proposed a space-time spreading code. The space-time spreading code can achieve higher code rate without performance loss.