  We have measured the specific heat of PrV$_2$Al$_{20}$ at very low
temperatures, using high quality single crystals with the residual resistivity
ratio ~ 20. The high-quality single crystals exhibit clear double transitions
at $T_{\rm Q} =$ 0.75 K and $T^* =$ 0.65 K. These transitions are clearer and
shift to higher temperature in higher quality single crystals. Besides, there
was no hysteresis in those transitions in warming and cooling process of the
heat capacity measurements. In the ordered state below $T^*$, the specific heat
shows a $T^4$ dependence, indicating the gapless mode associated with the
quadrupole and/or octupole ordering.
