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 $t \mapsto \{f(t^{1/m})\}^m$.