  Here we have illustrated the construction of a real structure on fuzzy sphere
$S^2_*$ in its spin-1/2 representation. Considering the SU(2) covariant Dirac
and chirality operator on $S^2_*$ given by Watamura et. al. in [6], we have
shown that the real structure is consistent with other spectral data for KO
dimension-4 fulfilling the zero order condition, where we find it necessary to
enlarge the symmetry group from SO(3) to the full orthogonal group O(3).
However the first order condition is violated thus paving the way to construct
a toy model for an SU(2) gauge theory to capture some features of physics
beyond standard model following Connes et.al. [9].
