We report the discovery of a second methanol maser in the Large Magellanic Cloud and we present the results of synthesis observations of this and the methanol maser detected previously. The second discovery was made using the Australia Telescope National Facility's 64-m Parkes radio telescope during an extensive maser search for 6.6-GHz maser emission from the 5_1_-6_0_ A^+^ transition in both Magellanic Clouds. Spectra were obtained towards 35 HII regions in the Large Magellanic Cloud and 13 regions in the Small Magellanic Cloud, and also on a 3-arcmin grid over an area 0.3^deg^ square, south of the 30 Doradus nebula. Parkes observations at 12.2 GHz towards the two maser sites yielded no detectable emission from the 2_0_-3_-1_, E methanol transition. The results suggest that methanol masers are less abundant in the Magellanic Clouds than in our Galaxy. Observations of the two masers with the Australia Telescope Compact Array showed one to be located near the continuum emission peak of the H II region MC18 (N11), while the other appeared to be centred near OH emission on the south-eastern boundary of MC23 (N105a).