In this paper, a novel scheme of bidirectional quantum teleportation is proposed, where two-qubit states are transferred into single qubit superposition by Alice and Bob respectively using controlled-NOT operation, meanwhile the four-qubit cluster states are utilized as quantum channel. Our main novelty, which is the significant difference from other schemes of bidirectional (controlled) quantum teleportation, is: as the receivers, the both legitimate users can reconstruct the target two-qubit states through the corresponding unitary operation and controlled-NOT transmission to realize the more efficient teleportation.