Let X be an L1-predual, non-separable in general. We show that the intrinsic Baire classes of X can be identified with the spaces of odd Baire functions on the set ext BX∗ of the extreme points of the dual unit ball BX∗ in the case when ext BX∗ satisfies some topological assumptions. This generalizes results of Lindenstrauss andWulbert from [On the classification of the Banach spaces whose duals are L1 spaces, J. Funct. Anal. 4 (1969), 332–349], Jellett in [On affine extensions of continuous functions defined on the extreme boundary of a Choquet simplex, Quart. J. Math. Oxford Ser. (1) 36 (1985), 71–73] and of ours in [Baire Classes of L1-preduals and C ∗-algebras, 2013. http://www.karlin.mff.cuni.cz/ spurny/articles.php].