The discretization of the metaplectic transform (MT) is considered, and it is shown that it can lead to completely new orthonormal bases (ONBs) for the signal space of square integrable functions. Two new classes of bases, the scale-and-shear bases and the translation-and-shear bases, are derived to demonstrate the discretization process. Besides generalizing the current methods of generating time-frequency-concentrated ONBs, MT bases possess extra degrees of freedom that can be used to match a wider variety of signals.