We report the first detection of a methanol maser in the 101–92 A− transition at 23.4 GHz, discovered during the H2O southern Galactic Plane Survey (HOPS) with the 22-m Mopra Radio Telescope. In the region covered by HOPS, the 23.4-GHz maser was found at only one location, G357.97−0.16, which was also a prominent source of maser emission in the J2–J1 E series near 25 GHz. The Australia Telescope Compact Array (ATCA) was used to follow up these detections at high angular resolution and prove the maser nature of the observed emission. The analysis shows that the new methanol maser at 23.4 GHz is a class I maser, which has properties similar to the 9.9- and 25-GHz masers (i.e. traces strong shocks with higher than average temperature and density). All class I masers were found to originate at the same spatial location (within the measurement uncertainty of 0.5 arcsec) in the vicinity of the dominant infrared source, but at a clearly distinct position from nearby OH, H2O and class II methanol masers at 6.7 GHz. All maser species are distributed approximately on a line, but it is not clear at present whether this has any physical significance. We also detected a weak (1.3 mJy) continuum source at 25 GHz near the OH maser (at the most northern site, associated with a class II methanol maser and an H2O maser renowned for its extremely wide spread of velocity components). The continuum source has not been reported at lower frequencies and is therefore a candidate hypercompact H ii region. We also used the ATCA to find the strongest and only the fifth known 9.9-GHz maser towards G357.97−0.16 and another 23.4-GHz maser towards G343.12−0.06 not seen in HOPS.