Let $f(t)$ be an operator monotone function
from the interval $(0, \infty)$ into itself.
In this note, we show that for
any positive integer $m,$
the matrices
\begin{equation*}
\left[ \frac{\{f(t_i)\}^m + \{f(t_j)\}^m}
{t_i^m + t_j^m} \right], \quad
\left[ \frac{\{f(t_i)\}^m - \{f(t_j)\}^m}
{t_i^m - t_j^m} \right]
\end{equation*}
are positive semidefinite
for all positive integers $n$
and $t_1, \dots, t_n$ in $(0, \infty)$;
that is, the Kwong matrices
$K_{\{f(t^{1/m})\}^m} (t_1, \dots, t_n)$ and
the Loewner matrices
$L_{\{f(t^{1/m})\}^m} (t_1, \dots, t_n)$
are positive semidefinite.
The former is a generalization of Kwong's result, and
the latter is an alternative proof for operator monotonicity
of the function $t \mapsto \{f(t^{1/m})\}^m$.