The onset of Taylor-Gortler instability induced by an impulsively started rotating cylinder with constant shear stress was analyzed by using propagation theory based on linear theory and momentary instability concept. It is well-known that the primary transient Couette flow is laminar but secondary motion sets in when the inner cylinder velocity exceeds a certain critical value. The dimensionless critical time τc to mark the onset of instability is presented here as a function of the modified Taylor number T. For the deep-pool case of small τ, since the inner cylinder velocity increases as Vi∝√t in the present impulsive shear system, the present system is more stable than impulsive started case (Vi=constant). Based on the present τc and the Foster’s [1969] comment, the manifest stability guideline is suggested.