  We have obtained an exact solution for the BPS domain wall junction for a N=1
supersymmetric theory in four dimensions and studied its properties. The model
is a simplified version of the N=2 SU(2) gauge theory with N_f=1 broken to N=1
by the mass of the adjoint chiral superfield. We define mode equations and
demonstrate explicitly that fermion and boson with the same mass have to come
in pairs except massless modes. We work out explicitly massless Nambu-Goldstone
(NG) modes on the BPS domain wall junction. We find that their wave functions
extend along the wall to infinity (not localized) and are not normalizable. It
is argued that this feature is a generic phenomenon of NG modes on domain wall
junctions in the bulk flat space in any dimensions. NG fermions exhibit a
chiral structure in accordance with unitary representations of (1, 0)
supersymmetry algebra where fermion and boson with the same mass come in pairs
except massless modes which can appear singly.
