In this paper, we propose a Differential Space-Time (S-T) block code with non-unitary constellations like QAM. This code works well for non-orthogonal and orthogonal S-T block codes, however, the previously proposed differential codes follow orthogonal block codes only. In addition, the receiver does not require any knowledge of channel power, signal power, or noise power to decode the proposed differential code and the decision is purely based on the two consecutively received data samples only. Whereas, in presivously suggested differential S-T codes for QAM, the receiver is required to estimate these quantities at each time from a large number of preceding data samples, before decision. The proposed differential S-T code also performs better as compared to the other differential S-T codes for non-unitary and unitary constellations.