  The generalized Chen's conjecture on biharmonic submanifolds asserts that any
biharmonic submanifold of a non-positively curved manifold is minimal (see
e.g., [CMO1], [MO], [BMO1], [BMO2], [BMO3], [Ba1], [Ba2], [Ou1], [Ou2], [IIU]).
In this paper, we prove that this conjecture is false by constructing
foliations of proper biharmonic hyperplanes in a 5-dimensional conformally flat
space with negative sectional curvature. Many examples of proper biharmonic
submanifolds of non-positively curved spaces are also given.
