Recent advances have shown that some biologically active non-coding RNAs (ncRNAs) are actually translated into polypeptides that have a physiological function as well. This paradigm shift requires adapted computational methods to predict this new class of ‘bifunctional RNAs’. Previously, we developed IRSOM, an open-source algorithm to classify non-coding and coding RNAs. Here, we use the binary statistical model of IRSOM as a ternary classifier, called IRSOM2, to identify bifunctional RNAs as a rejection of the two other classes. We present its easy-to-use web interface, which allows users to perform predictions on large datasets of RNA sequences in a short time, to re-train the model with their own data, and to visualize and analyze the classification results thanks to the implementation of self-organizing maps (SOM). We also propose a new benchmark of experimentally validated RNAs that play both protein-coding and non-coding roles, in different organisms. Thus, IRSOM2 showed promising performance in detecting these bifunctional transcripts among ncRNAs of different types, such as circRNAs and lncRNAs (in particular those of shorter lengths). The web server is freely available on the EvryRNA platform: https://evryrna.ibisc.univ-evry.fr.