The polynomial modal method (PMM) is one of the most powerful methods for modeling diffraction from lamellar gratings. In the present work, we show that applying it to the so-called matched coordinates leads to important improvement of convergence for crossed lamellar gratings with patterns that are not parallel to the coordinates' axes. After giving the new formulation of the PMM under matched coordinates in the general framework of biperiodic structures, we provide numerical examples to demonstrate the effectiveness of the proposed approach.