  The Schr\"odinger equation for the four-dimensional double singular
oscillator is separable in Eulerian, doble polar and spheroidal coordinates in
${\rm I R}^4$. It is shown that the coefficients for the expansion of double
polar basis in terms of the Eulerian basis can be expressed through the
Clebsch-Gordan coefficients of the group SU(2) analytically continued to real
values of their arguments. The coefficients for the expansions of the
spheroidal basis in terms of the Eulerian and double polar bases are proved to
satisfy three-term recursion relations.
