Using some results in J.-H. Shi and L. Lou [Acta Math. Sin., Engl. Ser. 16, 85-98 (2000; Zbl 0967.32007)], the authors prove that for a holomorphic self-map of the polydisc , the composition operator is compact on the Bloch space if and only if for every , there exists a , such that
whenever . This is an extension of result by K. Madigan and A. Matheson [Trans. Am. Math. Soc. 347, 2679-2687 (1995; Zbl 0826.47023))], to .