  We prove a version of Whitney's strong embedding theorem for isometric
embeddings within the general setting of the Nash-Kuiper h-principle. More
precisely, we show that any $n$-dimensional smooth compact manifold admits
infinitely many global isometric embeddings into $2n$-dimensional Euclidean
space, of H\"older class $C^{1,\theta}$ with $\theta<1/3$ for $n=2$ and
$\theta<(n+2)^{-1}$ for $n\geq3$. The proof is performed by Nash-Kuiper's
convex integration construction and applying the gluing technique of the
authors on short embeddings with small amplitude.
