Calculations are presented for the linear stability of isothermal, viscous Couette how of a radially magnetized ferrofluid in a narrow annulus between a long rotating inner cylinder and a stationary coaxial outer cylinder, In this prototype model of a rotary ferrofluid seal the countervailing influences of centrifugal diffusion and magnetodiffusion slowly create a radial gradient in the distribution of the colloidal particles, Provided that the strength of the radial magnetic field exceeds a critical threshold, steady Taylor vortex how is predicted to set in at Taylor numbers an order of magnitude smaller than the critical Taylor number of a simple diamagnetic liquid. Both the critical Taylor number and the critical wavenumber increase as the magnetic field strength increases. A remarkable feature is that the neutral curves for this long time scale Couette-Taylor instability are double valued.