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We consider beamforming schemes for the multi-antenna decode-and-forward (DF) relays that maximize the secrecy rate (SR) in the relay wiretap channel. Both full-duplex (FD) and half-duplex (HD) relays are considered, where the FD relay fights the loop-back self-interference while maximizing the SR. The HD relay beamforming is derived from the FD case as a byproduct. The facts that, the weaker link among the two hops in the DF relay network dominates, the throughput and the first hop is shared among the destination and the eavesdroppers make us divide the beamformer solution space into three separate regions. Since only two of the three regions effectively produce non-negative SR, separate beamformer designs for these two effective regions are provided. Numerical results reveal performance trade off of FD and HD modes in various channel configurations, where the two challenges of self-interference suppression and the protection from eavesdropping ask different requirements for the beamforming.