Unitary space-time modulation (USTM) is well-tailored for flat fading channels where neither the transmitter nor the receiver knows the fading coefficients. A systematic approach to designing USTM is proposed by Hochwald et al., which is not guaranteed full diversity and difficult to put into practice due to the large number of signal points in the two-dimensional constellation. Consequently, we modify the systematic method to search new unitary space-time coded 8PSK with full diversity. Simulation results indicate that the error performances of the searched codes are better than or at least the same as those of the USTM in [2].