Let Γ be a continuous pseudo group acting on a manifold M. Denote by (M, M’, ρ) a fibered manifold preserved by transformations in Γ. Then any f in Γ locally induces a local transformation f′ of M′. Denote by Γ/ρ the set of all such f′. Then it might seem natural to expect that Γ/ρ is a continuous pseudo group acting on M′. However the matter is not so simple. For instance, take f′ and g′ in Γ/ρ such that the composition f′°g′ can be defined. Then they can be lifted to local transformations f and g belonging to Γ.