Space-time codes are usually generated using a generator matrix with 2 columns and mod 4 operations for QPSK modulation with two transmit antennas. A Z4 convolutional code has also been used to represent these space-time codes. Another way of representing them is to use a conventional binary convolutional code of rate 2/4. The space-time code obtained in this way is in general different from the usual space-time codes. Simulations results have shown that the new codes can achieve an error performance very close to that of the best usual space-time codes and even outperform them. Furthermore, such a representation is more flexible and allows an easy implementation of space-time encoders and decoders for different numbers of transmit antennas. Only the rate of the convolutional code needs to be changed using the puncturing technique to accommodate these different schemes.