We propose a 2 × 2 space-time block code based on a trace criterion for 64-quadrature amplitude modulation (QAM). We introduce a method to easily calculate the trace norm of a space-time code for 64-QAM, and propose a new space-time code searched by this method. The error rate performance of the proposed code is compared with that of the Alamouti code. By comparison of the theoretical upper bounds, the proposed space-time code is better than the Alamouti code, when the number of receiving antennas is more than one. Moreover, bit error rate performance of the proposed code is compared with maximum likelihood decoding on perfect channel state information Rayleigh fading channels by computer simulations. These results show the proposed code almost outperforms the Alamouti code when the number of receive antennas is more than one, and the increased number of receiving antennas with our code is a decided advantage.