This paper proposes a new preprocessing scheme for rate-one quasi-orthogonal space-time block code (QO-STBC), which requires no channel state information at the transmitter. We consider QO-STBCs in real domain so as to utilize the real-valued multidimensional constellation. First, we derive a precoding matrix which makes the effective channel matrix of QO-STBC column-wise orthogonal. Surprisingly, the proposed scheme provides the channel gains identical to the singular values of the channel matrix of STBCs. Since singular value decomposition based precoding method provides better performance than other conventional maximum-likelihood decoding method in coded systems, the proposed scheme outperforms other STBC schemes in coded systems without feedback information, while reducing the decoding complexity dramatically. Second, we employ the rotated multidimensional constellation in order to achieve full diversity in uncoded systems. Unlike the previous works where heuristic approaches should be needed to obtain solutions in QO-STBC systems with more than four transmit antennas, the proposed precoding combined with the rotated multidimensional constellation provides an optimal solution based on analysis regardless of the number of transmit antennas.