  We have measured the magnetic field dependence of the paramagnetic to the
field-induced high temperature antiferroquadrupolar magnetically ordered phase
transition is CeB6 from 0 to 60 T using a variety of techniques. It is found
that the field-dependent phase separation line becomes re-entrant above 35 T
and below 10 K. Measurements of resonant ultra-sound, specific heat and neutron
diffraction show conclusively that the zero-field temperature-dependent phase
transition is to a state with no ordered dipole moments, but with second order
transition signatures in both sound attenuation and specific heat.
