We revisit the generalisation of the Guruswami-Sudan list decoding algorithm to Reed-Muller codes. Although the generalisation is straightforward, the analysis is more difficult than in the Reed-Solomon case. A previous analysis has been done by Pellikaan and Wu, relying on the theory of Groebner bases [2, 3]. We give a stronger form of the well-known Schwartz-Zippel Lemma [5, 4], taking multiplicities into account. Using this Lemma, we get an improved decoding radius.