Summary: We present a brief proof of a recently proved result [\textit{M. Ferrero} and \textit{C. Haetinger}, Quaest. Math. 25, No. 2, 249-257 (2002; Zbl 1009.16036), Corollary 1.4]. The main result states that if \(R\) is a prime ring of characteristic different from 2 and \(U\) is a Lie ideal of \(R\) where \(U\not\subset Z(R)\), the center of \(R\), \(u^2\in U\) for all \(u\in U\), and \(D\) is a Jordan higher derivation of \(U\) into \(R\), then \(D\) is a higher derivation of \(U\) into \(R\). This result extends a theorem of \textit{R. Awtar} [Proc. Am. Math. Soc. 90, 9-14 (1984; Zbl 0528.16020)].