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We introduce a new two-step relaying scheme based on superposition coding, SC-relaying. In Step 1, the source AS broadcasts a message, created by superposition coding, to the relay AR and the destination AD. After decoding the information from AS, AR relays a part of this message in Step 2, by using a codebook that is adapted to the link AR - AD. The information-theoretic design shows that the proposed scheme can improve the spectral efficiency, attaining almost optimal value. We demonstrate that the SC-relaying can be ported even to the case of uncoded systems, where it is shown how to select the transmission scheme in order to maximize the throughput between the source and the destination.