  We prove the non-rationality of a double cover of $\mathbb{P}^{n}$ branched
over a hypersurface $F\subset\mathbb{P}^{n}$ of degree $2n$ having isolated
singularities such that $n\ge 4$ and every singular points of the hypersurface
$F$ is ordinary, i.e. the projectivization of its tangent cone is smooth, whose
multiplicity does not exceed $2(n-2)$.
