  In the present work we show that the widely believed pathology of the
non-unitarity of anisotropic quantum cosmological models cannot be a generic
problem. We exhibit a non trivial example, a Bianchi-I model with an
ultrarelativistic fluid, that has a well behaved time independent norm. We also
show that a suitable operator ordering should produce time independent norms
for the wave packets in the case of other more realistic fluids as well.
