  We study real Lagrangian analytic surfaces in C^2 with a non-degenerate
complex tangent. Webster proved that all such surfaces can be transformed into
a quadratic surface by formal symplectic transformations of C^2. We show that
there is a certain dense set of real Lagrangian surfaces which cannot be
transformed into the quadratic surface by any holomorphic (convergent)
transformation of C^2. The divergence is contributed by the parabolic character
of a pair of involutions generated by the real Lagrangian surfaces.
