  We investigate the Bagger-Lambert-Gustavsson model associated with the
Nambu-Poisson algebra as a theory describing a single M5-brane. We argue that
the model is a gauge theory associated with the volume-preserving
diffeomorphism in the three-dimenisonal internal space. We derive gauge
transformations, actions, supersymmetry transformations, and equations of
motions in terms of six-dimensional fields. The equations of motions are
written in gauge-covariant form, and the equations for tensor fields have
manifest self-dual structure. We demonstrate that the double dimensional
reduction of the model reproduces the non-commutative U(1) gauge theory on a
D4-brane with a small non-commutativity parameter. We establish relations
between parameters in the BLG model and those in M-theory. This shows that the
model describes an M5-brane in a large C-field background.
