Material tensors pertaining to polycrystalline aggregates should manifest the influence of crystallographic texture on the material properties. A representation theorem on material tensors of weakly-textured polycrystals has been established by Man and Huang (2011) under the classical assumption in quantitative texture analysis that the orientation distribution function (ODF) is defined on the rotation group. By this theorem, a given material tensor can be expressed as a linear combination of an orthonormal set of irreducible basis tensors, with the components given explicitly in terms of texture coefficients and a set of undetermined material parameters.  In this talk, an extension of this representation theorem where the ODF is defined on the orthogonal group will be discussed. The extended theorem now covers all the 32 cases of point-group crystal symmetry.