In this paper,we consider the transmitter beamformer design at relays for a full-duplex two-way relay system,where the two sources are equipped with multiple antennas,and each one of the nearby relays is equipped with two antennas with one for transmission and the other for reception.Under the constraints of the limited transmit power and zero forcing nulling technique used at the relays,we propose two linear relay beamformer designs that are respectively to iteratively minimize the weighted mean square error of the two source nodes and maximize the signal to noise ratio of the smaller one of the two source nodes.The effectiveness and efficiency of the proposed designs are evaluated by numerical experiments in terms of the weighted sum rate and the CPU running time.