Considering a three-node multiple antenna relay system, this paper proposes a two-phase amplify-and-forward (AF) relaying protocol, which enables the autonomous relay to simultaneously harvest wireless power from the source information signal and from an energy signal conveyed by the destination. We first study this energy-flow-assisted (EFA) relaying in a single-input single-output (SISO) relay system and aim at maximizing the rate. By transforming the optimization problem into an equivalent convex form, a global optimum can be found. We then extend the protocol to a multiple antenna relay system. The relay processing matrix is optimized to maximize the rate. The optimization problem can be efficiently solved by eigenvalue decomposition, after linear algebra manipulation. It is observed that the benefits of the energy flow are interestingly shown only in the multiple antenna case, and it is revealed that the received information signal and the energy leakage at the relay can be nearly separated by making use of the signal space, such that the desired signal can be amplified with a larger coefficient.