Tunneling splitting of the vibrational ground state is calculated for a planar model of malonaldehyde by the instanton method of Mil'nikov and Nakamura with use of ab initio potential energy surface. The planar model gives much larger tunneling splitting than the previous full dimensional calculations, indicating a strong effect of the anharmonic coupling between the in-plane and out-of-plane modes. The anharmonicity is related to the Coriolis coupling between the OH stretching vibration and the pseudo-rotation of the hindered rotor. The present results suggest that the multidimensional effects should be carefully taken into account in the tunneling dynamics of polyatomic molecules. (C) 2004 Elsevier B.V. All rights reserved.