In this paper the author proves an extension of a theorem, due to \textit{L. Ness} [Am. J. Math. 106, 1281--1329 (1984; Zbl 0604.14006), theorem 6.2] to the case of real group actions. Let \(G\) be a real semisimple Lie group with Cartan-decomposed algebra \({\mathbf g}={\mathbf l}+{\mathbf p}\). A map \(m:{\mathbb P}(V) \rightarrow {\mathbf p}\) is defined as follows: \((m(x),\beta)_{\mathbf p}=\frac{(\beta v,v)}{(v,v)}\), for \(\beta \in {\mathbf p}\), and \(v\in V\). Let \(K\) be a maximal compact subgroup of \(G\). The authors shows that if \(x\) is a critical point of \(\| m\| ^2\), then \(\| m\| ^2| _{Gx}\) achieve a minimum at \(x\) and if nonempty, the critical set of \(\| m\| ^2\) contained in a \(G\)-orbit consists of a unique \(K\)-orbit.