  We obtain a new square function characterization of the weak Hardy space
$H^{p,\infty}$ for all $p\in(0,\iy)$. This space consists of all tempered
distributions whose smooth maximal function lies in weak $L^p$. Our proof is
based on interpolation between $H^p$ spaces. The main difficulty we overcome is
the lack of a good dense subspace of $H^{p,\infty}$ which forces us to work
with general $H^{p,\infty}$ distributions.
