  We solve explicitly a closed, linear loop equation for the SU(2) Wilson loop
average on a two-dimensional plane and generalize the solution to the case of
the SU(N) Wilson loop average with an arbitrary closed contour. Furthermore,
the flat space solution is generalized to any two-dimensional manifold for the
SU(2) Wilson loop average and to any two-dimensional manifold of genus 0 for
the SU(N) Wilson loop average.
