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We use Hurwitz-Radon matrices to construct a space-time code for parallel wireless mobile relays that are located anywhere between a source and a destination. Each relay receives a sequence of symbols (i.e., baseband signals corrupted by fading and noise) simultaneously from the source. These symbols are not decoded into information bits at the relays but are rearranged (i.e., space-time modulated) in their orders, amplitudes and phases according to the Hurwitz-Radon code. The relays do not exchange symbols with each other but forward the modified sequences of symbols in parallel to the destination. Our study shows that with R relays, an order of diversity around R/2 can be achieved, i.e., the averaged bit error rate is in the order of 1/SNRR2/ as opposed to 1/SNR for a single (regenerative) relay system. More than 10 dB power saving, from the baseline of the single relay system, can be achieved with eight (non-regenerative) relays.