  A generalisation of the Stieltjes relations for the Painlev\'e-IV
transcendents and their higher analogues determined by the dressing chains is
proposed. It is proven that if a rational function from a certain class
satisfies these relations it must be a solution of some higher Painlev\'e-IV
equation. The approach is based on the interpretation of the Stieltjes
relations as local trivial monodromy conditions for certain Schr\"odinger
equations in the complex domain. As a corollary a new class of the
Schr\"odinger operators with trivial monodromy is constructed in terms of the
Painlev\'e-IV transcendents.
