  We prove that the Cauchy problem for the Schr\"odinger-Korteweg-de Vries
system is locally well-posed for the initial data belonging to the Sovolev
spaces $L^2(\R)\times H^{-{3/4}}(\R)$. The new ingredient is that we use the
$\bar{F}^s$ type space, introduced by the first author in \cite{G}, to deal
with the KdV part of the system and the coupling terms. In order to overcome
the difficulty caused by the lack of scaling invariance, we prove uniform
estimates for the multiplier. This result improves the previous one by Corcho
and Linares.
