In the paper the simplification of construction of nonlinear normal vibration modes by Shaw-Pierre in power
series form is considered. The simplification can be obtained via change of variables in the equations o f motion
of dynamical system under consideration. This change of variables is constructed by means of so-called
ordered Schur matrix decomposition. As the result of the transformation there is no need in solving nonlinear
algebraic equations in order to evaluate coefficients of nonlinear normal mode.
