The anomaly due to the chiral fermions on the world-volume of the SO(3
2) five-brane is calculated. It is shown that this contribution has th
e correct structure for it to be cancelled by the variation of the cla
ssical world-volume action. The cancellation mechanism requires a Gree
n-Schwarz-like term in the classical action. The result confirms the f
ield content of the SO(32) five-brane proposed by Witten. (C) 1998 Els
evier Science B.V.