  We discuss the general behavior of the scattering amplitude with channel
couplings near the two-body threshold. It is known that the Flatt\'{e}
amplitude, which is often used in the analysis of experimental data involving
exotic hadrons, has some constraint in the near-threshold energy region. While
the M-matrix gives the general expression of the scattering amplitude, it is
not smoothly connected to the Flatt\'{e} amplitude, due to the property of the
determinant of the amplitude in channel space. In this paper, based on the
effective field theory, we propose new parametrization of the scattering
amplitude which gives the general expression near the threshold and has a
well-defined limit reproducing the Flatt\'{e} amplitude. We show that the
nonresonant background contribution exists in the general amplitude even in the
first order in the momentum. Finally, we quantitatively evaluate the cross
sections by changing the strength of the background contribution. We find that
the interference with the background term may induce a dip structure of the
cross section near the threshold, in addition to the peak and threshold cusp
structures.
