  Finite gauge transformations in double field theory can be defined by the
exponential of generalized Lie derivatives. We interpret these transformations
as `generalized coordinate transformations' in the doubled space by proposing
and testing a formula that writes large transformations in terms of derivatives
of the coordinate maps. Successive generalized coordinate transformations give
a generalized coordinate transformation that differs from the direct
composition of the original two. Instead, it is constructed using the Courant
bracket. These transformations form a group when acting on fields but,
intriguingly, do not associate when acting on coordinates.
