Let $k > 1$ be the fundamental discriminant, and let $\chi(n)$,
$\varepsilon$ and $h$ be the real primitive character modulo
$k$, the fundamental unit and the class number of the real
quadratic field $\mathbf{Q}(\sqrt{k} )$, respectively. And
let $[x]$ denote the greatest integer not greater than $x$.
¶ In [3], M.-G. Leu showed $h = \big[ \sqrt{k} / (2\log{\varepsilon})
\sum_{n=1}^k \chi(n) / n \big] + 1$ for all $k$, and
$h = \big[ \sqrt{k} / (2\log{\varepsilon}) \sum_{n=1}^{[k/2]} \chi(n) / n \big]$
in the case $k \neq m^2 + 4$ with $m \in \mathbf{Z}$.
¶ In this paper we will show
$h = \big[ \sqrt{k} / (2\log{\varepsilon}) \sum_{n=1}^{[k/2]} \chi(n) / n \big]$
for all fundamental discriminants
$k > 1$.