  It is well-known that the second homology group $H_2(\st)$ of the Steinberg
Lie algebra $\st$ is trivial when $n\geq 5$. In this paper, we will work out
$H_2(\st)$ explicitly for $n=3, 4$ which are not necessarily trivial.
Consequently, we obtained $H_2(sl_n(R))$ for $n=3, 4$.
