The demand for relay-transmission technologies has recently been increasing. We study relay transmission using multiband to reduce transmission delay and meet the increasing demand. In the relay transmission, the relay node initiates relay transmission while receiving data on another frequency band. However, despite its potential, the difference of data rates between reception and forwarding causes data loss from buffer overflow. To solve this problem, we propose an algorithm that selects appropriate channels, such that the transmission rates become as high as possible without buffer overflow, and evaluate the effectiveness of the proposal.