  We present a first-order symmetric hyperbolic system in the Ashtekar
formulation of general relativity for vacuum spacetime. We add terms from
constraint equations to the evolution equations with appropriate combinations,
which is the same technique used by Iriondo, Leguizam\'on and Reula [Phys. Rev.
Lett. 79, 4732 (1997)]. However our system is different from theirs in the
points that we primarily use Hermiticity of a characteristic matrix of the
system to characterize our system "symmetric", discuss the consistency of this
system with reality condition, and show the characteristic speeds of the
system.
