  In this note we show that for any proper action of a Banach--Lie group $G$ on
a Banach manifold $M$, the corresponding tangent maps $\g \to T_x(M)$ have
closed range for each $x \in M$, i.e., the tangent spaces of the orbits are
closed. As a consequence, for each free proper action on a Hilbert manifold,
the quotient $M/G$ carries a natural manifold structure.
