  The high energy limit of scattering amplitudes in the N=4 supersymmetric
Yang-Mills theory is studied by solving the corresponding BFKL equation in the
next-to-leading approximation. The gluon Green's function is analysed using a
newly proposed method suitable for investigating the contribution from higher
conformal spins. From this new approach complete agreement is obtained with the
results of Kotikov and Lipatov on conformal spins and angular dependence.
