In this work, we propose a novel method to increase the quality factor of extensional mode micromechanical resonators. The proposed resonator topology is suitable for integration in a silicon-based process to fabricate micromechanical filters and oscillators. It is a half-wavelength-long strip excited longitudinally by electrostatic forces, and it is isolated from the substrate by alternating with bars of a quarter wavelength long. This structure causes a large impedance mismatch between the resonator and the substrate and hence reduces the anchor loss considerably. The performance of the resonator is determined by finite element simulations. We introduce an equivalent electrical circuit to predict the performance of the resonator. The electrical model gives results consistent with the finite element simulations. The proposed resonator is expected to have a very small anchor loss resulting in a very high Q.