Foliation of the space $\mathfrak{sl}^*(n,\mathbb R)$ on coadjoint orbits

A method for the construction of parameters on coadjoint orbits in $\mathfrak{sl}^*(n,\mathbb R)$ is suggested. The method is based on the fact that the parameters are invariant with respect to the action of vector fields normal relative to the Killing form to the tangent space of an orbit. The construction of parameters is reduced to the solution of a homogeneous system of linear equations.