[en] If a grand Unified Theory with a compact unifying group G is spontaneously broken to H, magnetic monopoles are created. The fate of such an H-monopole under a subsequent breaking to K is contained in H is shown to depend on the behaviour of its non-Abelian charge Q introduced by Goddard, Nuyts, Olive: if Q belongs to the Lie algebra k of K, the monopole survives: if Q can be H-rotated to k, it can be converted. A necessary condition for an H-monopole to survie is that its Higgs charge satisfy a topological constraint