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(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 points(8-14). But these ideas remain untested experimentally, in part because supercooled water can be probed only above the homogeneous nucleation temperature T-H at which water spontaneously crystallizes. Here we report an experimental approach that is not restricted by the barrier imposed by T-H, 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(8). 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 P-c approximate to 0.1 GPa and temperature T-c approximate to 220 K.