  A new iteration method is represented to study the interior $L_{p}$
regularity for Stokes systems both in divergence form and in non-divergence
form. By the iteration, we improve the integrability of derivatives of
solutions for Stokes systems step by step; after infinitely many steps, $L_{p}$
regularity is achieved; and in each step, the maximal function method is used
where solutions and their derivatives are involved simultaneously in each
scale. The H\"{o}lder continuity of the coefficients in spatial variables is
assumed to compensate the different scalings between the solutions and their
derivatives.
