(The Eguchi-Hanson manifold) The Eguchi-Hanson metric $g$ is a complete Ricci flat metric on the cotangent bundle of $S^{2}$, which at infinity, becomes rapidly asymptotic to the metric cone on $\mathds{R}\mathds{P}(3)$ or equivalently to $\mathds{R}^{4}/\mathds{Z}_{2}$, where $\mathds{Z}_{2}$ acts on $\mathds{R}^{4}$ by $x\to-x$. When the metric $g$ is scaled down by $g\to r^{2}g$, with $r\to 0$, one obtains a family of Ricci flat manifolds whose Gromov-Hausdorff limit is $C(\mathds{R}\mathds{P}(3))=\mathds{R}^{4}/\mathds{Z}_{2}$. This is the simplest example which shows that even under the assumption of Ricci flatness and noncollapsing, Gromov-Hausdorff limit spaces can contain codimension 4 singularities.