  Answering to a recent question raised by Le\'{s}nik, Maligranda, and
Tomaszewski, we prove that there is an Orlicz function $\Phi$ with the upper
Matuszewska-Orlicz index equal to $1$ such that the Orlicz space $L_\Phi$ does
not satisfy Dunford-Pettis criterion of weak compactness.
