  We present a Matrix theory action and Matrix configurations for spherical
4-branes. The dimension of the representations is given by N=2(2j+1)
(j=1/2,1,3/2,...). The algebra which defines these configurations is not
invariant under SO(5) rotations but under SO(3) \otimes SO(2). We also
construct a non-commutative product for field theories on S^4 in terms of that
on S^2. An explicit formula of the non-commutative product which corresponds to
the N=4 dim representation of the non-commutative S^4 algebra is worked out.
Because we use S^2 \otimes S^2 parametrization of S^4, our S^4 is doubled and
the non-commutative product and functions on S^4 are indeterminate on a great
circle (S^1) on S^4. We will however, show that despite this mild singularity
it is possible to write down a finite action integral of the non-commutative
field thoery on S^4. NS-NS B field background on S^4 which is associated with
our Matrix S^4 configurations is also constructed.
