This paper presents a new approach for the design of film bulk acoustic resonators (FBARs) with high-quality factor ${Q}_{a}$ at antiresonant frequency ${f}_{a}$ . Lamb waves are among the main contributors to the loss of energy at ${f}_{a}$ and the deterioration of ${Q}_{a}$ . The targeted approach is an optimization process of a dual-step frame structure to alleviate the problem with Lamb waves at ${f}_{a}$ . Such a frame is a combination of two neighboring steps that have different acoustic impedances reflecting the two Lamb modes that carry the largest amount of energy. The dimensions of these steps are computed using the diffraction grating method. To do so, the dispersion curves of Lamb waves and their associated power flows are calculated using a global matrix method and the acoustic Poynting's Theorem. This results in an enhancement in ${Q}_{a}$ of nearly 82% for an FBAR with a dual-step frame in comparison with an FBAR with no frame, as well as a smoother electrical response, at frequencies above ${f}_{a}$ but below the resonant frequency ${f}_{r}$ spurious resonances are moderately increased.