  An infinite dimensional algebra which is a non-decomposable reducible
representation of $su(2)$ is given. This algebra is defined with respect to two
real parameters. If one of these parameters is zero the algebra is the
commutative algebra of functions on the sphere, otherwise it is a
noncommutative analogue. This is an extension of the algebra normally refered
to as the (Berezin) quantum sphere or ``fuzzy'' sphere. A natural indefinite
``inner'' product and a basis of the algebra orthogonal with respect to it are
given. The basis elements are homogenious polynomials, eigenvectors of a
Laplacian, and related to the Hahn polynomials. It is shown that these elements
tend to the spherical harmonics for the sphere. A Moyal bracket is constructed
and shown to be the standard Moyal bracket for the sphere.
