  We construct a family of steady solutions to the two-dimensional
incompressible Euler equation in a general bounded domain, such that the
vorticity is supported in two well-separated regions of small diameter and
converges to a pair of point vortices with opposite signs. Compared with
previous results, we do not need to assume the existence of an isolated local
minimum point of the Kirchhoff-Routh function. Moreover, due to their
variational nature, the solutions obtained are Lyapunov stable in $L^p$ norm of
the vorticity. The proofs are achieved by maximizing the kinetic energy over an
appropriate family of rearrangement classes of sign-changing functions and
studying the limiting behavior of the maximizers.
