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In multihop wireless networks, the quality of communications is degraded due to the relay transmissions over fading channels. Space-time code using multiple transmit antennas is an effective countermeasure for fading. For terminals which have only one antenna due to size/cost limitations, user cooperation has been introduced as a diversity technique. A new cooperative relaying scheme is proposed in order to combat the effects of fading in multihop communications among single antenna terminals. This scheme utilizes space-time code for cooperative relaying and is developed in both frequency-flat and frequency-selective fading channels for exploiting space and path diversity gain. By computer simulations, it is shown that the scheme can achieve almost full spatial diversity in multihop communications by both non-regenerative relaying with SNR estimation and regenerative relaying with error detection.