The Square surrounds the market green, which
has been the central point of Greenlaw since at least the late seventeenth
century, when it became county town.
During the eighteenth and nineteenth centuries,
two fairs were held here annually, in May and October. Also situated
in The Square were a weighing machine (tron), a well and a pillory.
The Town Hall, one of the few buildings
on the central green, was once also the County Court and the Castle
Inn opposite would have provided accommodation for lawyers and judges.