We report the results of a search for class II methanol masers at 37.7, 38.3 and 38.5 GHz towards a sample of 70 high-mass star formation regions. We primarily searched towards regions known to show emission either from the 107 GHz class II methanol maser transition, or from the 6.035 GHz excited OH transition. We detected maser emission from 13 sources in the 37.7 GHz transition, eight of these being new detections. We detected maser emission from three sources in the 38 GHz transitions, one of which is a new detection. We find that 37.7 GHz methanol masers are only associated with the most luminous 6.7 and 12.2 GHz methanol maser sources, which in turn are hypothesised to be the oldest class II methanol sources. We suggest that the 37.7 GHz methanol masers are associated with a brief evolutionary phase (of 1000-4000 years) prior to the cessation of class II methanol maser activity in the associated high-mass star formation region.
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