  It was shown in arXiv:0912.1456 that the large-$N$ reduction holds on group
manifolds in the sense that a large-$N$ gauge theory on a group manifold is
realized by a matrix model which is obtained by dimensionally reducing the
original theory to zero dimension. In this note, generalizing the above
statement, we show that a large-$N$ gauge theory on a group manifold is
equivalent to a theory which is obtained by reducing the original theory to its
coset space. This is analogous to the statement of the large-$N$ reduction on
flat spaces that large-$N$ gauge theories are independent of the volume.
