The global linear stability, where we assume no homogeneity in either of the spatial directions, of a two-dimensional laminar base flow through a spatially periodic converging–diverging channel is studied at low Reynolds numbers. A large wall-waviness amplitude is used to achieve instability at critical Reynolds numbers below ten. This is in contrast to earlier studies, which were at lower wall-waviness amplitude and had critical Reynolds numbers an order of magnitude higher. Moreover, our leading mode is a symmetry-breaking standing mode, unlike the traveling modes which are standard at higher Reynolds numbers. Eigenvalues in the spectrum lie on distinct branches, showing varied structure spanning the geometry. Our global stability study suggests that such modes can be tailored to give enhanced mixing in microchannels at low Reynolds numbers.