  We classify hypersurfaces of rank two of Euclidean space $\R^{n+1}$ that
admit genuine isometric deformations in $\R^{n+2}$. That an isometric immersion
$\hat f\colon\,M^n\to\R^{n+2}$ is a genuine isometric deformation of a
hypersurface $f\colon\, M^n\to\R^{n+1}$ means that $\hat f$ is nowhere a
composition $\hat f=\hat F\circ f$, where $\hat F\colon\,V\subset
\R^{n+1}\to\R^{n+2}$ is an isometric immersion of an open subset $V$ containing
$f(M)$.
