  We define in a systematic way, based on the light-cone collinear
factorization method, the chiral-odd generalized parton distributions (GPDs) of
a pseudoscalar hadron (such as the pi0) up to twist 5. For that, we introduce
the relevant matrix elements for 2-parton non-local operators, as well as
matrix elements for 3-parton non-local correlators. Their detailed
parametrization is fixed based on parity, charge conjugation and time reversal
invariance. This leads to the introduction of 20 real GPDs, whose symmetry
properties are explicitely given. The reduction of these GPDs to a minimal set
is performed by the use of constraints provided by QCD equations of motion and
rotation on the light-cone. We show that these 20 GPDs can be expressed through
8 GPDs which satisfy 4 integral sum rules. A surprising outcome of this
analysis is the fact that, when assuming the vanishing of 3-parton correlators,
as in the so-called Wandzura-Wilczek approximation, the whole set of GPDs
vanishes.
