  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 <~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 arcseconds. 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.
