Аннотация:We prove the statement that allows one extend the argument shifting procedure from symmetric algebra Sgl(d) of the Lie algebra gl(d) to the universal enveloping algebra Ugl(d). Namely, it turns out that the iterated quasi-derivations of the central elements in Ugl(d) commute with each other. Here quasi-derivations are certain linear operators on Ugl(d), projecting to the partial derivatives on symmetric algebra Sgl(d). This allows one better understand the structure of argument shift algebras (or Mishchenko-Fomenko algebras) in the universal enveloping algebra of gl(d).