  We show that 2D noncommutative harmonic oscillator has an isotropic
representation in terms of commutative coordinates. The noncommutativity in the
new mode, induces energy level splitting, and is equivalent to an external
magnetic field effect. The equivalence of the spectra of the isotropic and
anisotropic representation is traced back to the existence of SU(2) invariance
of the noncommutative model.
