  We give a new algorithm for the estimation of the cross-covariance matrix
$\mathbb{E} XY'$ of two large dimensional signals $X\in\mathbb{R}^n$, $Y\in
\mathbb{R}^p$ in the context where the number $T$ of observations of the pair
$(X,Y)$ is large but $n/T$ and $p/T$ are not supposed to be small. In the
asymptotic regime where $n,p,T$ are large, with high probability, this
algorithm is optimal for the Frobenius norm among rotationally invariant
estimators, i.e. estimators derived from the empirical estimator by cleaning
the singular values, while letting singular vectors unchanged.
