  It is well-known that the standard BCFW construction cannot be used for
on-shell amplitudes in effective field theories due to bad behavior for large
shifts. We show how to solve this problem in the case of the SU(N) non-linear
sigma model, i.e. non-renormalizable model with infinite number of interaction
vertices, using scaling properties of the semi-on-shell currents, and we
present new on-shell recursion relations for all on-shell tree-level amplitudes
in this theory.
