We propose to suppress acoustic wave coupling between a Si3N4 membrane resonator and its support structure through cascaded low-frequency resonators fabricated on the silicon substrate of the membrane. The on-chip silicon resonators are designed to ensure that the frequencies of their oscillatory motion are well separated from the mechanical modes of the membrane resonator. Using optical interferometry, we characterize the displacement response of the membrane frame with the vibration isolation; mechanical isolation >30 dB from the mounting surface is achieved. Thus, we reliably fabricate Si3N4 membrane resonators with mechanical quality factors of around 2×106 at room temperature.