  We study the large order and infinite order soliton of the coupled nonlinear
Schrodinger equation with the Riemann-Hilbert method. By using the
Riemann-Hilbert representation for the high order Darboux dressing matrix, the
large order and infinite order solitons can be analyzed directly without using
inverse scattering transform. We firstly disclose the asymptotics for large
order soliton, which is divided into four different regions -- the elliptic
function region, the non-oscillatory region, the exponential and algebraic
decay region. We verify the consistence between asymptotic expression and exact
solutions by the Darboux dressing method numerically. Moreover, we consider the
property and dynamics for infinite order solitons -- a special limitation for
the larger order soliton. It is shown that the elliptic function and
exponential region will disappear for the infinite order solitons.
