In current multi-hop relay networks (MRNs), normally the communication path is not optimized, especially when two mobile stations (MSs) attached to the same relay station (RS) need to communicate with each other. In this paper, a novel data transmission scheme: administrable and controllable local forwarding for OFDMA-TDD based two-hop relay cellular networks, is proposed. In the local forwarding mode, data transmission between two MSs attached to the same RS is forwarded without necessarily being sent to the base station (BS). Thereby the spectral efficiency is improved. And then two cost based relay selection schemes (RSSs) are proposed for the efficient usage of local forwarding mode. The first is a modified traditional RSS (RSS-MT), which implements local forwarding after relay selection. And the second is a local forwarding-based RSS (RSS-LF), which takes the advantages of the local forwarding into account during relay selection. Numerical and simulation results show that the local forwarding transmission schemes can improve the system capacity greatly. Moreover, the performance of RSS-LF is shown to be superior to that of RSS-MT.