This paper proposes an application of splitting source-node power for a two-phase cooperative relaying system where the transmit powers of the source and the relay node are individually constrained. In the proposed usage, the limited source power is divided into two parts that are used in the first and the second phase. Unlike conventional relaying methods, in the second phase the source retransmits its signal with the split power and, at the same time, the relay forwards the signal received at the first phase, which causes interference between the signals. In order to avoid the intervention, so-called a co-phasing weight for aligning the phases of the two signals is used at at the source before the second transmission. The forwarding operation at the relay however is exactly the same as the conventional techniques. Optimal power-splitting as well as the co-phasing weight is provided in this paper. With numerical investigation, the proposed power-splitting is shown to significantly improve the achievable throughput as well as reduce the outage probability compared with the conventional individual power allocation.