We first prove a certain kind of splitting theorem for an equifocal submanifold
with non-flat section in a simply connected symmetric space of compact type, where an equifocal
submanifold means a submanifold with parallel focal structure. By using the splitting theorem,
we prove that there exists no equifocal submanifold with non-flat section in an irreducible simply
connected symmetric space of compact type whose codimension is greater than the maximum of
the multiplicities of roots of the symmetric space or the maximum added one. In particular, it
follows that there exists no equifocal submanifold with non-flat section in some irreducible simply
connected symmetric spaces of compact type and that there exists no equifocal submanifold with
non-flat section in simply connected compact simple Lie group whose codimension is greater than
two.