—In most of the existing space–time code designs, achieving full diversity is based on maximum-likelihood (ML) decoding at the receiver that is usually computationally expensive and may not have soft outputs. Recently, Zhang–Liu–Wong introduced Toeplitz codes and showed that Toeplitz codes achieve full diversity when a linear receiver, zero-forcing (ZF) or minimum mean square error (MMSE) receiver, is used. Motivated from Zhang–Liu–Wong’s results on Toeplitz codes, in this paper, we propose a design criterion for space–time block codes (STBC), in which information symbols and their complex conjugates are linearly embedded, to achieve full diversity when ZF or MMSE receiver is used. The (complex) orthogonal STBC (OSTBC) satisfy the criterion as one may expect. We also show that the symbol