Long chains in the Rudin-Frolík order for uncountable cardinals

We point out that a construction by Butkovičová of a chain of length ${\mathfrak{c}}^{+}$ in the Rudin-Frolík order on $\beta \omega$ can easily be adapted to produce, given an uncountable cardinal $\kappa$, a chain of length $(2^{\kappa }{)}^{+}$ in the Rudin-Frolík order on $\beta \kappa$.