MANY of the low-temperature thermodynamic properties of water, such as heat capacity and isothermal compressibility, exhibit anomalous behaviour that tends to diverge in the supercooled state(1,2). On the basis of molecular dynamics simulations(3,4), these phenomena have recently been attributed to the influence of a critical point terminating the temperature-pressure coexistence line separating low- and high-density amorphous ices, But the fact that water tends to lose its anomalous behaviour(5) in the pressure range predicted for the new critical point poses problems for such an interpretation. Moreover, the phase diagram derived from these simulations contrasts sharply with another conjecture, whereby it is argued that at atmospheric pressure no thermodynamically continuous path exists between low-density amorphous ice and normal water(6). Here I report the results of a series of molecular dynamics simulations at constant (approximately atmospheric) pressure, which show that both ideas can be reconciled by relocating the critical point to negative pressures. The resulting phase diagram is not only simpler, but also accounts for the transition of water from a fragile to a strong liquid in the supercoooled region7,8.