Summary: ``We investigate the existence of nonradial positive solutions for a critical semilinear biharmonic problem defined on a unit ball. The solution is obtained as a minimizer of the quotient functional associated to the problem restricted to appropriate subspaces of $H^2\cap H^1_0$ invariant for the action of a subgroup of $\scr O(N)$. By making use of more careful estimates and some new arguments, we extend Serra's result in [E. Serra, Calc. Var. Partial Differential Equations {\bf 23} (2005), no.~3, 301--326; MR2142066 (2006f:35100)] to the biharmonic case.''