  In this paper, we consider linear elliptic systems from composite materials
where the coefficients depend on the shape and might have the discontinuity
between the subregions. We derive a function which is related to the gradient
of the weak solutions and which is not only locally piecewise H\"{o}lder
continuous but locally H\"{o}lder continuous. The gradient of the weak
solutions can be estimated by this derived function and we also prove local
piecewise gradient H\"{o}lder continuity which was obtained by the previous
results.
