  Let $a_1,\dotsc,a_n$ be a permutation of $[n]$. Two disjoint order-isomorphic
subsequences are called \emph{twins}. We show that every permutation of $[n]$
contains twins of length $\Omega(n^{3/5})$ improving the trivial bound of
$\Omega(n^{1/2})$. We also show that a random permutation contains twins of
length $\Omega(n^{2/3})$, which is sharp.
