We present a proof of Ky Fan\u27s combinatorial lemma on labellings of triangulated spheres that differs from earlier proofs in that it is constructive. We slightly generalize the hypotheses of Fan\u27s lemma to allow for triangulations of Sn that contain a flag of hemispheres. As a consequence, we can obtain a constructive proof of Tucker\u27s lemma that holds for a more general class of triangulations than the usual version
