  Let $(M,g)$ be a non-locally conformally flat compact Riemannian manifold
with dimension $N\ge7.$ We are interested in finding positive solutions to the
linear perturbation of the Yamabe problem $$-\mathcal L_g u+\epsilon
u=u^{N+2\over N-2}\ \hbox{in}\ (M,g) $$ where the first eigenvalue of the
conformal laplacian $-\mathcal L_g $ is positive and $\epsilon$ is a small
positive parameter. We prove that for any point $\xi_0\in M$ which is
non-degenerate and non-vanishing minimum point of the Weyl's tensor and for any
integer $k$ there exists a family of solutions developing $k$ peaks collapsing
at $\xi_0$ as $\epsilon$ goes to zero. In particular, $\xi_0$ is a non-isolated
blow-up point.
