On the basis of earlier experimental studies the intermetallic compound Mn2Au has been characterized as a nonmagnetically ordered material. Here we report the results of first-principles calculations based on local spin-density approximation that describes Mn2Au to have a narrow band ground state with rigid local moments on the Mn sites. Calculations of the interatomic exchange constants based on the magnetic force theorem and a Monte Carlo modeling of the resulting Heisenberg-like Hamiltonian predict a high Neel temperature of ∼1600 K. This temperature is considerably higher than for the other known high-temperature antiferromagnetic L10-type Mn based binary alloys used in magnetic storage applications.