  We show how $Z$-invariance in the chiral Potts model provides a strategy to
calculate the pair correlation in the general integrable chiral Potts model
using only the superintegrable eigenvectors. When the distance between the two
spins in the correlation function becomes infinite it becomes the square of the
order parameter. In this way, we show that the spontaneous magnetization can be
expressed in terms of the inner products of the eigenvectors of the $N$
asymptotically degenerate maximum eigenvalues. Using our previous results on
these eigenvectors, we are able to obtain the order parameter as a sum almost
identical to the one given by Baxter. This gives the known spontaneous
magnetization of the chiral Potts model by an entirely different approach.
