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We propose a new full rate space-time block code for a three transmit antenna system that is orthogonal when using a special modulation scheme, called "triple QPSK". This space-time block code achieves full diversity gain when used with "triple QPSK" modulation. The performance of this new space-time block code is evaluated by using Monte Carlo simulation and union bounding techniques. Simulation results match the results obtained from the union bound analysis very well at reasonable signal to noise ratios. We conclude that the new space-time block code achieves better performance when compared with conventional space-time block codes.