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We have used the Australia Telescope National Facility Mopra 22-m antenna tosearch for 37.7-GHz (7(-2) - 8(-1}E) methanol masers towards a sample of thirtysix class II methanol masers. The target sources are the most luminous class IImethanol masers not previously searched for this transition, with isotropicpeak 12.2-GHz maser luminosity greater than 250 Jy/kpc^2 and isotropic peak6.7-GHz maser luminosity greater than 800 Jy/kpc^2. Seven new 37.7-GHz methanolmasers were detected as a result of the search. The detection rate for 37.7-GHzmethanol masers towards a complete sample of all such class II methanol masersites south of declination -20 deg is at least 30 percent. The relatively highdetection rate for this rare methanol transition is in line with previouspredictions that the 37.7-GHz transition is associated with a late stage of theclass II methanol maser phase of high-mass star formation. We find that thereis a modest correlation between the ratio of the 6.7- and 37.7-GHz maser peakintensity and the 6.7- and 12.2-GHz maser peak intensity (correlationcoefficient 0.63 in a log-log plot). We detected one new 38.3-GHz (6(2) -5(3)A-) methanol maser towards G335.789+0.174. This is only the fourth sourcefor which maser emission has been detected in this transition and it is theonly one for which emission is not also observed in the 38.5-GHz 6(2) - 5(3)A+transition.

Testing maser-based evolutionary schemes: A new search for 37.7-GHz methanol masers