  We perform atom interferometry using the Zeeman sublevels of a spin-2
Bose-Einstein condensate of $^{87}$Rb. The observed fringes are strongly
peaked, and fringe repetition rates higher than the fundamental Ramsey
frequency are found in agreement with a simple theory based on spin rotations.
With a suitable choice of initial states, the interferometer could function as
a useful tool for magnetometry and studies of spinor dynamics in general.
