A new approach is presented for the design of fulldiversity multilayer space-time error correcting codes (STECCs), for two transmitters. In addition to the linearity which is exploited to transmit linear combinations of forward error correcting (FEC) codewords, the proposed approach uses spacetime threading concepts to obtain high diversity and coding gain on each block-fading multiple-input multiple-output channel corresponding to a space-time codeword. We present in this paper the construction of 2×3 multilayer STECCs, which outperform the previously known ones.