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Piezoelectric micro-machined ultrasonic transducers (pMUTs) for air-coupled ultrasound applications were fabricated using aluminum nitride (AlN) as the active piezoelectric material. Earlier pMUTs based on a fully clamped membrane design suffer from high sensitivity to residual stress, causing large variations in the operating frequency, and have a reduced dynamic range due to nonlinearity at large drive voltages. Here we evaluate a new design based on a membrane that is supported by three flexures and a thin oxide layer, aimed to release residual stress, extend the mechanical dynamic range and improve the acoustic coupling. The acoustic performance of this flexurally suspended design is compared with a fully clamped one, showing a piston-like mode shape, which translates to improved output sound pressure.