We propose a new differential modulation scheme for multiple-antenna systems based on square space-time block codes (STBC) when neither the transmitter nor the receiver knows channel state information. Compared with the known differential unitary space-time modulation (DUSTM), the proposed constellations generally have multiple amplitudes and do not have group properties. This generalization potentially allows the spectral efficiency to be increased by carrying information not only on orientations (or phases) but also on amplitudes. Two non-coherent decoders, optimal differential decoder (DD) and near-optimal DD, are derived for flat Rayleigh fading channels. Particularly, the near-optimal DD inherits the decomposition decoding property retained by STBC with coherent receiver and thus has linear complexity. Compared with the best-known cyclic group constellations designed for DUSTM, our proposed constellations with the near-optimal DD have significantly lower probability of error and lower decoding complexity.