  We show that the M-canonical map of an n-dimensional complex projective
manifold X of Kodaira dimension two is birational to an Iitaka fibration for a
computable positive integer M. M depends on the index b of a general fibre F of
the Iitaka fibration and on the Betti number of the canonical covering of F, In
particular, M is a universal constant if the dimension n is smaller than or
equal to 4.
