  In this paper, we obtain a geometric result for composite materials related
to elliptic and parabolic partial differential equations. In the classical
papers Li and Vogelius (2000), and Li and Nirenberg (2003), they assumed that
for any scale and for any point there exists a coordinate system such that the
boundaries of the individual components of a composite material locally become
$C^{1,\gamma}$-graphs. We prove that if the individual components of a
composite material are composed of $C^{1,\gamma}$-boundaries then such a
coordinate system in Li and Vogelius (2000), and Li and Nirenberg (2003)
exists, and therefore obtaining the gradient boundedness and the piecewise
gradient H\"{o}lder continuity results for linear elliptic systems related to
composite materials.
