  We find that there is an alternative possibility to define the chirality
operator on the fuzzy sphere, due to the ambiguity of the operator ordering.
Adopting this new chirality operator and the corresponding Dirac operator, we
define Connes' spectral triple on the fuzzy sphere and the differential
calculus. The differential calculus based on this new spectral triple is
simplified considerably. Using this formulation the action of the scalar field
is derived.
