The problem of blind channel estimation under space-time block coded (STBC) transmissions is addressed. Firstly, a blind channel estimation criterion that generalizes previous works is proposed. The technique is solely based on second-order statistics (SOS) and if the channel is identifiable, the estimate is obtained as the main eigenvector of a generalized eigenvalue problem (GEV). Secondly, a new transmission technique is proposed to solve the indeterminacies associated to the blind channel estimation problem. The technique is based on the combination of different STBCs, and it can be reduced to a nonredundant precoding consisting in the rotation or permutation of the transmit antennas. Unlike other previous approaches, the proposed technique does not imply a penalty in the transmission rate or capacity of the STBC system, while it is able to avoid the ambiguities in many practical cases, which is illustrated by means of some simulation examples.