  In this remark, we give another approach to the local well-posedness of
quadratic Schr\"odinger equation with nonlinearity $u\bar u$ in $H^{-1/4}$,
which was already proved by Kishimoto \cite{kis}. Our resolution space is
$l^1$-analogue of $X^{s,b}$ space with low frequency part in a weaker space
$L^{\infty}_{t}L^2_x$. Such type spaces was developed by Guo. \cite{G} to deal
the KdV endpoint $H^{-3/4}$ regularity.

Analysis of PDEs