We have used the Australia Telescope Compact Array ( ATCA ) to search for a number of centimetre wavelength methanol transitions which are predicted to show weak maser emission towards star formation regions . Sensitive , high spatial and spectral resolution observations towards four high-mass star formation regions which show emission in a large number of class II methanol maser transitions did not result in any detections . From these observations we are able to place an upper limit of \stackrel { \raisebox { -0.86 pt } { $ \textstyle < $ } } { \sim } 1300K on the brightness temperature of any emission from the 3 _ { 1 } A ^ { + } – 3 _ { 1 } A ^ { - } , 17 _ { -2 } – 18 _ { -3 } E ( v _ { t } = 1 ) , 12 _ { 4 } – 13 _ { 3 } A ^ { - } , 12 _ { 4 } – 13 _ { 3 } A ^ { + } and 4 _ { 1 } A ^ { + } – 4 _ { 1 } A ^ { - } transitions of methanol in these sources on angular scales of 2 ^ { \prime \prime } . This upper limit is consistent with current models for class II methanol masers in high-mass star formation regions and better constraints than those provided here will likely require observations with next-generation radio telescopes .