Abstract: The Stable Extrapolation Two-Time-Level Scheme (SETTLS) has been implemented in the GRAPES regional model to determine the trajectory and nonlinear terms. To make the scheme stable, selecting a relatively warm reference temperature is necessary. The first-order decentered averaging of the linear terms of the previous version of the GRAPES relaxes the restriction of a relatively warm reference temperature but its large weight results in a significant damping for the low-wavenumber modes. Therefore, a second-order accuracy decentering of the linear terms and warmer reference temperature are applied in the GRAPES model. The results from the ideal experiments show that the new semi-implicit semi-Lagrangian scheme is stable and leads to much less damping than the original time integration scheme.