To effectively reduce the inter-relay interference (IRI) in two-path successive relaying, two beamforming schemes are proposed in this paper, utilizing multiple-antenna relay nodes. Specifically, the two cooperation nodes perform receive combining of the source signal and transmit beamforming of the relayed signal alternately in the successive relaying process. As a result, the IRI between them can be effectively suppressed, thanks to the additional degree of freedom provided by the multiple-input multiple-output inter-relay channel. In the first beamforming scheme, the source-to-destination signal-to-interference-plus-noise ratios (SINR) of separate paths are maximized with approximation, leading to a minimum variance distortionless response beamformer under the high SINR condition. To further improve the system performance, noting that the received SINRs of the two paths have impact on each other due to the mutual coupling of the beamformers, the sum of mean squared errors from these two transmission paths is minimized in the second scheme. Based on this performance criterion, a suboptimal beamformer design is developed numerically through cyclic minimization of the sum of mean squared error cost function. Simulation results demonstrate the superiority of both proposed beamforming schemes in terms of symbol error rate and the achievable system rate, in particular, at high IRI levels.