We present two ordered successive interference cancellation (OSIC) schemes using the QR decomposition for the double space-time transmit diversity (DSTTD) system. These are designed by zero-forcing (ZF) and minimum-mean-squared error (MMSE) criteria. The computational complexity is significantly reduced by utilizing special structure of the channel matrix. These schemes re(luire fewer computations than previously known OSIC schemes. Especially the ZF-OSIC-QR achieves approximately 8% lower computational efforts than the twostage linear ZF detection with 2.4 dB performance advantage at the bit error rate (BER) of 10^-4.