A new thermodynamic potential of seawater is found with the temperature variable being Conservative Temperature.  From this thermodynamic potential all the thermodynamic variables of seawater can be calculated.  This thermodynamic potential adds to the two other thermodynamic potentials, the Gibbs function and the Helmholtz function, which have been known for more than a century.  Because of the advantages of using Conservative Temperature instead of in situ temperature, it is expected that the new thermodynamic potential will replace the Gibbs function in oceanography.  The new thermodynamic potential can be expressed as the sum of two parts, one depending on enthalpy and the other on entropy, and it is shown that there is a clean separation between the thermodynamic properties such as specific volume and sound speed that depend only on enthalpy, and those that depend also on enthalpy such as in situ temperature.