Although liquid water has been the focus of intensive research for over 100 years, a coherent physical picture that unifies all of the known anomalies of this liquid *RF 1-3* is still lacking. Some of these anomalies occur in the supercooled region, and have been rationalized on the grounds of a possible retracing of the liquid-gas spinodal (metastability limit) line into the supercooled liquid region [4-7] or alternatively the presence of a line of first-order liquid-liquid phase transitions in this region which ends in a critical point [8-14]. But these ideas remain untested experimentally, in part because supercooled water can be probed only above the homogeneous nucleation temperature TH at which water spontaneously crystallizes. Here we report an experimental approach that is not restricted by the barrier imposed by TH, involving measurement of the decompression-induced melting curves of several high-pressure phases of ice in small emulsified droplets. We find that the melting curve for ice IV seems to undergo a discontinuity at precisely the location proposed for the line of liquid-liquid phase transitions . This is consistent with, but does not prove, the coexistence of two different phases of (supercooled) liquid water. From the experimental data we calculate a possible Gibbs potential surface and a corresponding equation of state for water, from the forms of which we estimate the coordinates of the liquid-liquid critical point to be at pressure Pc [nearly =] 0.1 GPa and temperature Tc [nearly =] 220 K.