In a conventional opportunistic transmit (COT) cooperative relaying system, only the relays that receive signal-to-noise ratio (SNR) from the source and that exceed the threshold transmit to the destination. The COT system, however, only considers the SNR of the source-relay (S-R) path regardless that the SNR of the relay-destination (R-D) path is the opportunistic transmission condition. For that reason, it is not guaranteed that all the transmitted signals from relays exceed the threshold at the destination. Therefore we propose a double opportunistic transmit (DOT) cooperative relaying system - when both of the received SNR from a source and from a destination exceed the threshold, the relay transmits to the destination. It is shown that the proposed DOT system reduces power consumption by 6.9, 20.9, 32.4, and 41.4 % for K =3, 5, 7, and 9, respectively under the given condition of $P_{out}=1{ imes}10^{-3}$ and $overline{gamma}_{SR}/Gamma_{SR}$=30 dB, compared to the COT system. We noticed that the performance of the DOT system is superior to that of the COT system for the identical number of active transmit relays under the same condition of the normalized average SNR of $overline{gamma}_{RD}/Gamma_{RD}$.