Non-radial modes are excited in classical pulsators, both in Cepheids and in RR Lyrae stars. Firm evidence comes from the first-overtone pulsators, in which an additional shorter period mode is detected with characteristic period ratio falling between 0.60 and 0.65. For first-overtone Cepheids, three separate sequences populated by nearly 200 stars are formed in the Petersen diagram, i.e. the diagram of period ratio versus longer period. For first-overtone RR Lyrae stars (RRc stars), the situation is less clear. A dozen or so such stars are known. They form a clump in the Petersen diagram without any obvious structure. Interestingly, all first-overtone RR Lyrae stars for which precise space-borne photometry is available, show the additional mode, which suggests that its excitation is common. Motivated by these results, we searched for non-radial modes in the OGLE-III photometry of RRc stars from the Galactic bulge. We report the discovery of 147 stars, members of a new group of double-mode, radial–non-radial-mode pulsators. They form a clear and tight sequence in the Petersen diagram, with period ratios clustering around 0.613 and a signature of a possible second sequence with higher period ratio (0.631). The scatter in period ratios of the already known stars is explained as due to population effects. Judging from the results of space observations, this still mysterious form of pulsation must be common among RRc stars and our analysis of the OGLE data just touches the tip of the iceberg.