In this paper, we propose a new beamforming technique for signal-to-noise ratio maximization in nonregenerative multiple-input multiple-output cooperative relaying systems where a non-negligible direct link between the source and the destination exists. Instead of conventional optimal schemes resorting to an iterative method such as a gradient ascent algorithm, we provide a simple closed form solution for source-relay joint beamformer designs. To this end, we apply the error decomposition property which allows us to separate the problem into two phases. Then, we propose a new beamforming scheme which adaptively aligns the transmit signal to each phase depending on the channel condition. From simulation results, we confirm that the proposed technique obtains the near-optimal performance.