A key component in the itinerant-electron theory of spin waves in ferr
omagnetic transition metals is the model used for the exchange matrix
elements. The present work describes how, within a tight-binding forma
lism, the complete set of matrix elements can be expressed in terms of
a minimal number of parameters by invoking all the constraints impose
d by the symmetry of the system. The theory is used to predict the spi
n-wave spectrum of hcp cobalt. It is found that the spectrum (at least
in the Gamma-A direction) is rather insensitive to model details thro
ughout most of the wave-vector range apart from a small. region around
the reciprocal lattice points.