  We demonstrate how to separate the rotational degrees of freedom in a quantum
N-body problem completely from the internal ones. It is shown that any common
eigenfunction of the total orbital angular momentum ($\ell$) and the parity in
the system can be expanded with respect to $(2\ell+1)$ base-functions, where
the coefficients are the functions of the internal variables. We establish
explicitly the equations for those functions, called the generalized radial
equations, which are $(2\ell+1)$ coupled partial differential equations
containing only $(3N-6)$ internal variables.
