  Let $K$ be a compact Hausdorff space with weight w$(K)$, $\tau$ an infinite
cardinal with cofinality cf$(\tau)$ and $X$ a Banach space. In contrast with a
classical theorem of Cembranos and Freniche it is shown that if cf$(\tau)>$
w$(K)$ then the space $C(K, X)$ contains a complemented copy of $c_{0}(\tau)$
if and only if $X$ does.
  This result is optimal for every infinite cardinal $\tau$, in the sense that
it can not be improved by replacing the inequality cf$(\tau)>$ w$(K)$ by
another weaker than it.
