  Physical properties of DyB$_4$ have been studied by magnetization, specific
heat, and ultrasonic measurements. The magnetic entropy change and the
ultrasonic properties in the intermediate phase II indicate that the degeneracy
of internal degrees of freedom is not fully lifted in spite of the formation of
magnetic order. The ultrasonic attenuation and the huge softening of $C_{44}$
in phase II suggests existence of electric-quadrupolar (orbital) fluctuations
of the 4$f$-electron. These unusual properties originate from the geometrical
quadrupolar frustration.
