Space-time turbo codes have both advantages of space-time codes and turbo codes, and the space-time turbo code proposed by Su and Geraniotis is known to achieve full coding rate and full antenna diversity. This paper presents some improvements of their space-time turbo code in a two-antenna configuration. We first propose a new condition for full antenna diversity which imposes less constraints on the interleaver. Next, by applying a method used to improve turbo trellis-coded modulation to the space-time turbo code, we propose a new decoding algorithm which utilizes more precise estimates on extrinsic information. Simulation results show that the proposed condition assures full antenna diversity and the new decoding algorithm provides a better performance than that of Su and Geraniotis'.