  This paper reconsider the problem of a Proca field in the exterior of a
static black hole. The original Bekenstein's demonstration on the vanishing of
this field, based on an integral identity, is improved by using more natural
arguments at the event horizon. In particular, the use of the so-called
standard integration measure in the horizon is fully justified. Accordingly,
the horizon contribution to the Bekenstein integral identity is more involved
and its vanishing can be only established using the related Einstein equations.
With the new reasoning the ``no-hair'' theorem for the Proca field now rest on
better founded grounds.
