Transmit beamforming (BF) with reliable channel state information at the transmitter (CSIT) can improve the system performance significantly. On the other hand, for unreliable CSIT pure space-time coding outperforms transmit BF. In this paper, the combination of time-reversal space-time block codes (TR-STBCs) and transmit BF for transmission over frequency-selective fading channels is considered. The proposed scheme takes the reliability of the CSIT into account in an optimum way. For unreliable CSIT, the proposed scheme yields the same diversity gains as a TR-STBC, whereas for reliable CSIT significant BF gains can be obtained in addition to the diversity gain of the TR-STBC.