  A reduction method of ODEs not possessing Lie point symmetries makes use of
the so called $\lambda$-symmetries (C. Muriel and J. L. Romero, \emph{IMA J.
Appl. Math.} \textbf{66}, 111-125, 2001). The notion of covering for an ODE
$\mathcal{Y}$ is used here to recover $\lambda$-symmetries of $\mathcal{Y}$ as
nonlocal symmetries. In this framework, by embedding $\mathcal{Y}$ into a
suitable system $\mathcal{Y}^{\prime}$ determined by the function $\lambda$,
any $\lambda$-symmetry of $\mathcal{Y}$ can be recovered by a local symmetry of
$\mathcal{Y}^{\prime}$. As a consequence, the reduction method of Muriel and
Romero follows from the standard method of reduction by differential invariants
applied to $\mathcal{Y}^{\prime}$.
