We present the results of the first complete unbaised survey of the Galactic Plane for 6035-MHz excited-state hydroxyl masers undertaken as part of the Methanol Multibeam Survey . These observations cover the Galactic longitude ranges 186 ^ { \circ } < l < 60 ^ { \circ } including the Galactic Centre . We report the detection of 127 excited-state hydroxyl masers within the survey region , 47 being new sources . The positions of new detections were determined from interferometric observations with the Australia Telescope Compact Array . We discuss the association of 6035-MHz masers in our survey with the 6668-MHz masers from the MMB Survey , finding 37 likely CH _ { 3 } OH - ex-OH maser pairs with physical separations of \leq 0.03pc and 55 pairings separated by \leq 0.1pc . Using these we calculate for the first time an excited-state hydroxyl maser life time of between 3.3 \times 10 ^ { 3 } and 8.3 \times 10 ^ { 3 } years . We also discuss the variability of the 6035-MHz masers and detection rates of counterpart 6030-MHz excited-state hydroxyl masers ( 28 % of our sample having detection at both frequencies ) .