  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 methanol-excited-state hydroxyl
masers maser pairs with physical separations of <=0.03pc and 55 pairings
separated by <=0.1pc. Using these we calculate for the first time an
excited-state hydroxyl maser life time of between 3.3x10^3 and 8.3x10^3 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).
