  In this paper we give a geometric interpretation of a reduction method based
on the so called $\lambda$-variational symmetry (C. Muriel, J.L. Romero and P.
Olver 2006 \emph{Variational $C^{\infty}$-symmetries and Euler-Lagrange
equations} J. Differential equations \textbf{222} 164-184). In general this
allows only a partial reduction but it is particularly suitable for the
reduction of variational ODEs with a lack of computable local symmetries. We
show that this method is better understood as a nonlocal symmetry-reduction.
