Applying a rapid start-stop to the outer cylinder of the Couette-Taylor system, structures approximately aligned with the axis have been observed. In recent experiments the instability has been observed to arise during the decelerating phase. It was observed only with a narrow gap (d=6 mm, r_i/r_o=0.97), and the dependence of the wavelength on the initial acceleration rate was recorded. Here we report numerical observation of this instability. It is found that linear instability exists in 2-dimensional (z-independent) calculations, but that it could easily be missed in this idealised case -- the component of the perturbation which grows rapidly during the deceleration phase is rapidly destroyed in the acceleration phase, relative to other disturbances, and is thus swamped. Introducing the disturbance at later stages helps to isolate the growing mode. In the classic work of Coles (1965), similar instability was observed, but mentioned only in passing. In a footnote, its appearance was attributed, 'probably', to Tollmein instability. Initial calculations suggest this to be unlikely, given a discrepancy of wavelengths, but further calculations are in progress. We briefly discuss the instability with respect to other unsteady Taylor--Couette flows, with modulated cylinder rotation or abrupt stoppage, e.g Singh and Prigent (2021).