  In the last decade five new ice phases were experimentally prepared. Two of
them are empty clathrate hydrates and three of them represent hydrogen ordered
counterparts of previously known disordered ice phases. Here, we report on
hydrogen ordering in ice VI samples upon cooling at pressures up to 1.8 GPa.
Using calorimetry, dielectric relaxation spectroscopy, Raman spectroscopy, and
powder X-ray diffraction we provide evidence for the existence of a second
hydrogen ordered phase related to ice VI, that we call ice {\beta}-XV. This
phase is more ordered than ice XV by 14% and directly transforms to ice XV
above 103K and to ice VI above 129K. That is, upon heating an
order->order->disorder transition is experienced. The new phase is thus
thermodynamically more stable than ice XV requiring a new stability region in
the phase diagram of water. Raman spectroscopy indicates ice XV and ice
{\beta}-XV to be different in terms of symmetry and space group. The activation
energies for dielectric relaxation are 45 kJ mol-1 in ice {\beta}-XV compared
to 18 kJ mol-1 in ice XV. Powder X-ray data show the oxygen network to be the
one of ice VI. The ordering of hydrogen atoms induces a significant peak shift
to lower d-spacings at d=0.265 nm in ice {\beta}-XV, whereas for ice XV shifts
to higher d-spacings are found. This present work represents a unique
experimental realization of a second electric ordering in an ice phase.
