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Let $G$ be a compact and connected semisimple Lie group and $\Sigma$ an invariant control systems on $G$. Our aim in this work is to give a new proof of Theorem 1 proved by Jurdjevic and Sussmann in [6]. Precisely, to find a positive time $s_{\Sigma }$ such that the system turns out controllable at uniform time $s_{\Sigma }$. Our proof is different, elementary and the main argument comes directly from the definition of semisimple Lie group. The uniform time is not arbitrary. Finally, if $A={\bigcap }_{t>0}A(t,e)$ denotes the reachable set from arbitrary...