A magnetic field penetrates a superconductor through an array of 'vortices', each of which carries one quantum of flux that is surrounded by a circulating supercurrent. In this vortex state, the resistivity is determined by the dynamical properties of the vortex 'matter'. For the high-temperature copper oxide superconductors (see ref.1 for a theoretical review), the vortex phase can be a 'solid', in which the vortices are pinned, but the solid can 'melt' into a 'liquid' phase, in which their mobility gives rise to a finite resistance. (This melting phenomenon is also believed to occur in conventional superconductors, but in an experimentally inaccessible part of the phase diagram.) For the case of YBa2Cu3O7, there are indications of the existence of a critical point, at which the character of the melting changes. But neither the thermodynamic nature of the melting, nor the phase diagram in the vicinity of the critical point, has been well established. Here we report measurements of specific heat and magnetization that determine the phase diagram in this material to 26 T, well above the critical point. Our results reveal the presence of a reversible second-order transition above the critical point. An unusual feature of this transition-namely, that the high-temperature phase is the less symmetric in the sense of the Landau theory-is in accord with theoretical predictions of a transition to a second vortex-liquid phase.