  Separation of variables by means of the orbit method is implemented to
integrable systems on coadjoint orbits in an $\mathfrak{sl}(4)$ loop algebra.
This is a development and a kind of explanation for Sklyanin's procedure of
separation of variables. It is shown that points on a spectral curve serve as
variables of separation for two integrable systems living on two generic orbits
embedded into a common manifold. These orbits are endowed with different
nonsingular Lie-Poisson brackets. Explicit expressions for the case of
$\mathfrak{sl}(4)$ loop algebra are given.
