  Constructing the Semi - Unitary Transformation (SUT) to obtain the
supersymmetric partner Hamiltonians for a one dimensional harmonic oscillator,
it has been shown that under this transformation the supersymmetric partner
loses its ground state in T^{4}- space while its eigen functions constitute a
complete orthonormal basis in a subspace of full Hilbert space.
  Keywords: Supersymmetry, Superluminal Transformations, Semi Unitary
Transformations.
  PACS No: 14.80Lv
