  Let $E_C$ be the hypergeometric system of differential equations satisfied by
Lauricella's hypergeometric series $F_C$ of $m$ variables. We show that the
monodromy representation of $E_C$ is irreducible under our assumption
consisting of $2^{m+1}$ conditions for parameters. We also show that the
monodromy representation is reducible if one of them is not satisfied.
