A fundamental reality throughout the space and laboratory plasmas is the existence of magnetic field-aligned flows. It is usually believed that the spatial transverse shear in the parallel flow destabilizes many low-frequency instabilities and this may be the origin of low-frequency oscillations in the ionosphere. Here we show that this notion of the destabilizing influence of the shear in the parallel flow canbe changed altogether if one takes the effect of the flow curvature(second spatial derivative) into account. The transverse curvature in the parallel flow can overcome the destabilizing influence of the shear and can render the low-frequency ion temperature gradient-type instabilities stable.