  We prove the existence of an infinite sequence of distinct non-radial nodal
$G-$invariant solutions for the following critical nonlinear elliptic problem:
$({\mathrm{P}})\quad {*{20}c} {-\Delta u = |u|^{4/(n-2)}u},\quad u\in
C^2(\mathbb{R}^n), \quad n\geq3}$
