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Transmit antenna selection (TAS) is usually applied to multiple-input multiple-output (MIMO) systems because it does not require additional radio frequency (RF) chains which are quite expensive. In MIMO decode-and-forward (DF) relay networks, both source-destination and source-relay-destination paths should be simultaneously considered to find an effective source TAS (STAS). In this paper, a new STAS is proposed based on both channel state information and transmission scheme for the MIMO DF relay networks. It is also shown that the proposed STAS which selects MSS antennas among MS transmit antennas at the source can achieve full diversity regardless of the value of MSS. Simulation results show that the proposed STAS has better average bit error probability (BEP) performance than other STASs. Also, the proposed STAS with MSS=1 has lower cost, complexity, overhead, and BEP than the STAS with MSS > 1 using full-rate full-diversity space-time block codes with the same total transmit power.