In Trans. Am. Math. Soc. 213, 305-314 (1975; Zbl 0312.55020), \textit{K. Y. Lam} proves, among other things, an immersion result for the real flag manifold \(G_{{\mathbb{R}}}(n_ 1,...,n_ s)=O(n_ 1+...+n_ s)/O(n_ 1)x...xO(n_ s)\) where O(n) is the real orthogonal group. His result is a special case of the following more general observation. Proposition 1. Let G be a compact, connected semisimple Lie group and H a closed subgroup. Then either G/H is a \(\pi\)-manifold (and so immerses in codimension one) or G/H immerses in \({\mathbb{R}}^{\dim({\mathfrak g})}\), where \({\mathfrak g}\) is the Lie algebra of G.