Recent experiments on the antiferromagnetically ordered compound CeAs suggest that the order parameter is almost conserved in this system. The spin-wave spectra display quadratic dispersion which is unusual in an antiferromagnet. The author obtains an exact solution for the spin-wave spectra in an order-parameter-preserving FCC antiferromagnet and explain the origin of the quadratic dispersion. The relevance of these results to the experimental situation is also discussed.