  Degrees of freedom for high-order binary constrained flows of soliton
equations admitting $2\times 2$ Lax matrices are $2N+k_0$. It is known that
$N+k_0$ pairs of canonical separated variables for their separation of
variables can be introduced directly via their Lax matrices. In present paper
we propose a new method to introduce the additional $N$ pairs of canonical
separated variables and $N$ additional separated equations. The Jacobi
inversion problems for high-order binary constrained flows and for soliton
equations are also established. This new method can be applied to all
high-order binary constrained flows admitting $2\times 2$ Lax matrices.
