  This paper is a continuation of our previous study on the long time behavior
of solution to the nonlinear Schr"odinger equation with higher order
anisotropic dispersion (4NLS). We prove the long range scattering for (4NLS)
with the quadratic nonlinearity in two dimensions. More precisely, for a given
asymptotic profile $u_{+}$, we construct a solution to (4NLS) which converges
to $u_{+}$ as t to infinity, where $u_{+}$ is given by the leading term of the
solution to the linearized equation of (4NLS) with a logarithmic phase
correction.
