An exact solution of domain wall junction is obtained in a four-dimensional N = 1 supersymmetric U(1) * U(1)' gauge theory with three pairs of chiral superfields which is motivated by the N = 2 SU(2) gauge theory with one flavor perturbed by an adjoint scalar mass. The solution allows us to evaluate various quantities including a new central charge Y_k associated with the junction besides Z_k which appears already in domain walls. We find that the new central charge Y_k gives a negative contribution to the mass of the domain wall junction whereas the central charge Z_k gives a dominant positive contribution. One has to be cautious to identify the central charge Y_k alone as the mass of the Junction.
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