  We present numerical results on the hydrodynamic stability of coalescing
binary stars in the first post Newtonian(1PN) approximation of general
relativity. We pay particular attention to the hydrodynamical instability of
corotating binary stars in equilibrium states assuming the stiff polytropic
equation of state with the adiabatic constant $\Gamma=3$. In previous 1PN
numerical studies on corotating binary stars in equilibrium states, it was
found that along the sequence of binary stars as a function of the orbital
separation, they have the energy and/or angular momentum minima where the
secular instability sets in, and that with increase of the 1PN correction, the
orbital separation at these minima decreases while the angular velocity there
increases. In this paper, to know the location of the innermost stable circular
orbit(ISCO), we perform numerical simulations and find where the hydrodynamical
instability along the corotating sequences of binary sets in. From the
numerical results, we found that the dynamical stability limit seems to exist
near the energy and/or angular momentum minima not only in the Newtonian, but
also in the 1PN cases. This means that the 1PN effect of general relativity
increases the angular frequency of gravitational waves at the ISCO.
