Abstract — A channel-eigenvector invariant space-time constellation (CEI-STC) is a set of matrices such that the product of any pairwise difference matrix and its complex conjugate transpose is a scalar matrix. The pairwise error probability of a multi-antenna system equipped with the CEI-STC does not depend on the eigenvectors of the channel matrix. It may, however, depend on the eigenvalues of the channel. The maximum cardinality of a CEI-STC whose entries are restricted to a finite set is studied. A lower bound and an upper bound on the maximum cardinality are obtained. I