The system RMI is a purely relevance logic based on the intuitive ideas of relevance domains and degrees of significance. In this paper, we show that unlike the systems of Anderson and Belnap, RMI has a corresponding cut-free, Gentzen-type version. This version manipulates hyperse-quents (i.e. finite sequences of ordinary sequents), and no translation of those hypersequents into the language of RMI is possible. This shows that RMI is multiple-conclusioned in nature and hints on possible applications of it to the study of parallelism.