This article deals with a nonrelativistic study of a D-dimensional sup
erintegrable system, which generalizes the ordinary isotropic oscillat
or system. The coefficients for the expansion between the hyperspheric
al and Cartesian bases (transition matrix), and vice versa, are found
in terms of the SU(2) Clebsch-Gordan coefficients analytically continu
ed to real values of their arguments. The diagram method, which allows
one to construct a transition matrix for an arbitrary dimension, is d
eveloped.