Summary: W. Mader [J. Graph Theory 65, No. 1, 61–69 (2010; Zbl 1234.05145)] conjectured that for every positive integer \(k\) and every finite tree \(T\) with order \(m\), every \(k\)-connected, finite graph \(G\) with \(\delta(G) \geq \lfloor \frac{3}{2} k \rfloor + m - 1\) contains a subtree \(T^\prime\) isomorphic to \(T\) such that \(G - V(T^\prime)\) is \(k\)-connected. In the same paper, Mader proved that the conjecture is true when \(T\) is a path. A. A. Diwan and N. P. Tholiya [Discrete Math. 309, No. 16, 5235–5237 (2009; Zbl 1202.05023)] verified the conjecture when \(k = 1\). In this paper, we will prove that Mader’s conjecture is true when \(T\) is a star or double-star and \(k = 2\).