  The star-product between functions enable us to take the large $N$ limit in a
controlled way. At finite $N$ it serves as a substitute for matrix
multiplications. Non-abelian gauge theory can be deconstructed from lower
dimensional gauge theories using star-products. In this paper we extend the
star-product to a star-three-product. We then apply the star-three-product to
realize hermitian three-algebra of ABJM theory. We define a fuzzy three-torus.
We deconstruct Abelian M five-brane in a constant background three-form
potential on a fuzzy three-torus. We deconstruct non-Abelian extensions which
might be related with multiple M five branes. We also mention the fuzzy
three-sphere case.
