  State-of-the-art methods in multidimensional NLTE radiative transfer are
based on the use of local approximate lambda operator within either Jacobi or
Gauss-Seidel iterative schemes. Here we propose another approach to the
solution of 2D NLTE RT problems, Forth-and-Back Implicit Lambda Iteration
(FBILI), developed earlier for 1D geometry. In order to present the method and
examine its convergence properties we use the well-known instance of the
two-level atom line formation with complete frequency redistribution. In the
formal solution of the RT equation we employ short characteristics with
two-point algorithm. Using an implicit representation of the source function in
the computation of specific intensities, we compute and store the coefficients
of the linear relations J = a + bS between the mean intensity J and the
corresponding source function S. The use of iteration factors in the 'local'
coefficients of these implicit relations in two 'inward' directions, along with
the update of the source function in other two, 'outward', directions leads to
four times faster solution than the Jacobi's one. Moreover, the update made in
all four consecutive sweeps of the grid leads to an acceleration by a factor of
6-7 compared to the Jacobi iterative scheme.
