  We construct a fuzzy $S^4$, utilizing the fact that ${\bf CP}^3$ is an $S^2$
bundle over $S^4$. We find that a fuzzy $S^4$ can be described by a
block-diagonal form whose embedding square matrix represents a fuzzy ${\bf
CP}^3$. We discuss some pending issues on fuzzy $S^4$, i.e., precise
matrix-function correspondence, associativity of the algebra, and etc.
Similarly, we also obtain a fuzzy $S^8$, using the fact that ${\bf CP}^7$ is a
${\bf CP}^3$ bundle over $S^8$.
