  We obtain a new explicit expression for the noncommutative (star) product on
the fuzzy two-sphere which yields a unitary representation. This is done by
constructing a star product, $\star_{\lambda}$, for an arbitrary representation
of SU(2) which depends on a continuous parameter $\lambda$ and searching for
the values of $\lambda$ which give unitary representations. We will find two
series of values: $\lambda = \lambda^{(A)}_j=1/(2j)$ and
$\lambda=\lambda^{(B)}_j =-1/(2j+2)$, where j is the spin of the representation
of SU(2). At $\lambda = \lambda^{(A)}_j$ the new star product $\star_{\lambda}$
has poles. To avoid the singularity the functions on the sphere must be
spherical harmonics of order $\ell \leq 2j$ and then $\star_{\lambda}$ reduces
to the star product $\star$ obtained by Preusnajder. The star product at
$\lambda=\lambda^{(B)}_j$, to be denoted by $\bullet$, is new. In this case the
functions on the fuzzy sphere do not need to be spherical harmonics of order
$\ell \leq 2j$. Because in this case there is no cutoff on the order of
spherical harmonics, the degrees of freedom of the gauge fields on the fuzzy
sphere coincide with those on the commutative sphere. Therefore, although the
field theory on the fuzzy sphere is a system with finite degrees of freedom, we
can expect the existence of the Seiberg-Witten map between the noncommutative
and commutative descriptions of the gauge theory on the sphere. We will derive
the first few terms of the Seiberg-Witten map for the U(1) gauge theory on the
fuzzy sphere by using power expansion around the commutative point $\lambda=0$.
