We extend, to the quantum domain, the results obtained in [Nucl. Phys. B 885 (2014) 150] and [Phys. Lett. B 738 (2014) 405] concerning Niederer’s transformation for the Pais–Uhlenbeck oscillator. Namely, the quantum counterpart (an unitary operator) of the transformation which maps the free higher derivatives theory into the Pais–Uhlenbeck oscillator is constructed. Some consequences of this transformation are discussed.