  In this paper we introduce the open Waring rank of a form of degree d in n
variables and prove the that this rank in bounded from above by
\binom{n+d-2}{d-1} - \binom{n+d-6}{d-3} whenever n, d >= 3. This proves the
same upper bound for the classical Waring rank of a form, improving the result
of [BBS] and giving, as far as we know, the best upper bound known.
