Transceiver designs for multiple-input multiple-output (MIMO) two-way relaying are being actively explored. Most of the state-of-the-art studies optimize a system-wide objective function subject to the transmit power constraints on the two source nodes and the relay. Transceiver designs with quality-of-service (QoS) constraints have lacked attention in two-way relaying literature. In this paper, we study a MIMO transceiver design, based on the generalized singular value decomposition, that allocates power at the source and relay nodes to optimize the following per-stream rate-constrained objectives: 1) network transmit power, and 2) sum-rate. In addition, we also maximize the rate of the transmit stream with the worst signal-to-noise ratio. Through extensive numerical evaluations, we demonstrate the superior performance of proposed design over the existing ones, not only with QoS constraints but also without them. © 2002-2012 IEEE.