  SUSY partnership between singular potentials often breaks down. Via
regularization it can be restored on certain ad hoc subspaces of Hilbert space
[Das and Pernice, Nucl. Phys. B 561 (1999) 357]. Within the naturally
complexified (so called PT symmetric) quantum mechanics we show how SUSY
between strongly singular harmonic oscillators can completely be
re-established. Our recipe leads to a new form of the bosonic creation and
annihilation operators and proves continuous near the usual regular (i.e.,
linear harmonic) limit.
