In the U(3) x U(3) chiral perturbation theory, on-shell physical amplitudes are independent of any nonlinear realization of chiral symmetry. However, if one is restricted to eight pseudo-Goldstone bosons, then the nonlinear realization scheme in chiral SU(3) x SU(3) must be of the exponential form. The isospin violating decay η + 3π is employed as an example to elaborate on this phenomenon. We also consider a case in which the physical amplitude is independent of the realization scheme chosen, while the soft-pion theorem is.